In Star Wars Miniatures there are many different levels of Rock-Paper-Scissors. This post will attempt to categorize as many as possible.

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BASIC SQUAD TYPES
Basic squad types have been categorized using the terms Rock-Paper-Scissors as follows:

Rock squads are squads that focus on high-cost, high-HP, high-damage figures. They are great at taking out any single enemy, often in one activation.

Paper squads are squads that "cover" the map with many small pieces. Swarm squads. They are great at beating Rock squads because the Rock squads only take out a few swarm pieces at a time. Meanwhile, all of the swarm pieces can focus their fire on the Rock pieces and wear them down pretty quickly.

Scissors squads are squads that spread damage out to many different figures. They don't deal as much damage to a single figure, so they have trouble with Rock squads, but because they spread their damage out they can easily defeat a Paper squad.

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CHARACTER OFFENSE TYPES: SHOOTING, MELEE, DIRECT DAMAGE
Characters can often be described as melee, non-melee (shooting), or direct damage pieces. Further, they can be viewed as offensive (beat stick), defensive (tank), or balanced. All of these categories can also be viewed as a type of Rock-Paper-Scissors.

Non-melee (shooting) pieces usually have the advantage when they can keep their distance. Melee attackers have to be adjacent to attack them and most (not all) direct damage requires range 6. Their down side is that they usually have lower stats (attack/defense/HP) for their cost.

Melee pieces typically come with good stats (attack/defense/HP) for their cost. In general, if they can catch up to an equal-cost shooter, they can take care of him pretty quickly.

True direct damage pieces are pretty rare. Usually, direct damage is an option that is on a non-melee or melee piece. The direct damage is usually lower damage than an attack but has the advantage of ignoring a character's high defense or defensive special abilities such as Parry or Evade. However, even having a direct damage option will increase a character's cost.

CHARACTER DEFENSE TYPES: VULNERABLE, MELEE, NON-MELEE
Speaking of defensive abilities, those will also increase a character's cost. There are melee defensive abilities such as Parry; non-melee defensive abilities such as Evade or Cloaked; damage reducers such as Force Bubble or Vonduun Crab Armor. Characters may have more than one type. Characters with strong defensive abilities are often referred to as tanks. Darth Zannah and General Obi-Wan Kenobi are the strongest examples.

In summary, for offense we have Melee, Non-Melee, and Direct Damage. And for defense we have Vulnerable, Melee, Non-Melee. (And of course, in reality characters often have some combination of these to varying degrees.)

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OFFENSE VERSUS DEFENSE
Let's look at example characters for each combination of some standard offense/defense types. In each case, offense is listed first and then defense...

Melee/Vulnerable: Zekk (no defense)
Melee/Non-melee: Quinlan Vos, Double Agent (Force Cloak)
Melee/Melee: General Grievous, Hero of Hypori (Parry)
Non-melee/Vulnerable: Aurra Sing, Assassin
Non-melee/Non-melee: Morrigan Corde (Evade)
Non-melee/Melee: Corso Riggs (Flight lets him get away when based.) All shooters have the Melee defense ability called "stay away and shoot", so very few have additional defenses against Melee. Flight and Self Destruct are about the only ones. Only 2 shooters have Parry, and both also have melee attack options (Huntress and Pre Vizsla).
Direct/Vulnerable: Jaden Korr (Lightning/Push/Grip)
Direct/Non-melee: Alema Rar (Lightning, Force Cloak)
Direct/Melee: Darth Plagueis (Corruption, Parry)

This is where things get more complicated. In theoretical head-to-head matchups:

Zekk has an advantage over Quinlan Vos, Double Agent and Morrigan Corde and Alema Rar because they all have a higher cost due to their non-melee defenses (Evade or Force Cloak), which are useless against Zekk. Zekk has an advantage over Jaden Korr because while neither has defense to speak of, Zekk can do more attack damage for lower cost. Jaden's cost is increased for his direct damage options, which aren't needed against a vulnerable Zekk. He beats Alema for the same reason.

Quinlan Vos, Double Agent has an advantage over Aurra Sing, Assassin and Morrigan Corde due to his Force Cloak defense. And an advantage over Alema Rar since he gets more damage output. Alema's cost is increased due to direct damage options and Force Cloak, neither of which are needed against Quin.

General Grievous, Hero of Hypori has an advantage in melee matchups against Zekk or Quin since he has the melee defense. Also has the advantage against Alema Rar, since her cost includes Force Cloak, which is useless against GGHoH.

I won't go into detail on the others, but in summary:
Zekk beats Quin, Morrigan, Jaden, Alema
Quin beats Aurra, Morrigan, Alema
GGHoH beats Zekk, Quin, Alema
Aurra beats GGHoH, Corse Riggs, Jaden Korr, Darth Plagueis
Morrigan beats Aurra, Corso, Darth Plagueis
Jaden doesn't beat anyone in this list. He beats uber-tanks like GOWK or Darth Zannah who have extra defense built into their cost. Jaden gets to ignore all that defense.
Alema beats Morrigan and Corso
Plagueis beats Quin and Grievous

Note that this is all "in theory" how things should work. Where I say character A "beats" character B, that means that in a head-to-head matchup character A should be a better choice for its points than character B. It doesn't necessarily mean character A actually wins, because in reality, all of the above characters have additional abilities, are of different power levels, and vary in whether they are undercosted or overcosted. (If I didn't mention that one beats the other, it means that relative to their cost the characters are roughly equal when facing each other.)

All of this is just to illustrate how the rock-paper-scissors tends to work with regard to types of offense/defense.

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DEGREE OF DEFENSE: TANKS VERSUS OVERWHELMING FORCE
You will notice that I mentioned tanks above but did not use them as one of the types of defense. A tank is someone that is very difficult to defeat due to defensive abilities and/or stats. General Obi-Wan Kenobi and Darth Zannah are the most famous examples, but there are others as well. Tanks have defense against both melee and non-melee and/or have damage reducers such as Shields, Dark Armor, or Damage Reduction.

Characters that are very tank-like have a higher cost, but they often do very well against traditional damage dealers and gain an advantage that way.

Overwhelming Force-type abilities ignore defensive abilities, so characters with those abilities do well against tanks. Many defensive abilities only work on attacks, so direct damage options get around many tanks, but not all. (For example, Damage Reduction works on all damage, not just attacks.) However, Overwhelming Force-type abilities and direct damage options raise a character's cost.

Traditional attackers cost less than Overwhelming Force-type characters, so unless you are facing a tank, traditional attackers are probably the better choice.

In summary:
TANK beats TRADITIONAL ATTACKER beats OVERWHELMING-FORCE beats TANK

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COMMANDER-EFFECTS

If you pay for a commander effect, that's usually a good thing. But CEs can be suppressed. If you pay for CE suppression and there aren't any to suppress, you wasted points paying for something useless. So in general:

COMMANDER-EFFECTS beats NO-CEs beats CE-SUPPRESSION beats COMMANDER-EFFECTS

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FORCE-POWERS

If you pay for a Force power, that's usually a good thing. But FPs can be suppressed. If you pay for FP suppression and there aren't any to suppress, you wasted points paying for something useless. So in general:

FORCE-POWERS beats NO-FPs beats FP-SUPPRESSION beats FORCE-POWERS
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DOOR CONTROL

Override is a powerful ability, but a map with minimal doors or an opponent extensively using Satchel Charge makes Override useless (and a waste of points). On the other hand, bringing lots of Satchel Charge against a squad with no door control means you spent points on tech instead of combat, leaving you at a disadvantage there.

OVERRIDE beats NO-DOOR-CONTROL beats SATCHEL-CHARGE beats OVERRIDE

In practice, Override beats No-Door-Control so severely (potential auto-win) that almost no one ever goes with no door control at all, since the cost savings of going without it adds up to just a few points. So really the NO-DOOR-CONTROL option should probably say LOW-DOOR-CONTROL. But the idea here is the same as with CEs or FPs. If you spend points countering something that you don't run into anyway, then you wasted points on it that could have been spent elsewhere instead.

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BALANCE VERSUS EXTREME

In any of the above rock-paper-scissors aspects of the game, you have a choice to go for an extreme or go for more balance. If you go for an extreme, you risk easy wins and easy losses. For example, Extreme Scissors should crush Extreme Paper. Extreme Overwhelming-Force should crush Extreme Tank. The alternative is to go for balance in a squad or choose a balanced character that has multiple options. With a balanced squad, you may not have any auto-wins (and may even be at a disadvantage in most games), but hopefully you don't have any auto-losses either. You can build a balanced squad by mixing different types of extreme characters or taking several balanced characters.

Updated. Let me know if you think of any others.

Bump. Just because it's interesting theory to think about.

Wow, yeah, that is a nasty squad.

How did I miss reading this thread? Thanks for necro/bumping it

@thehutts,
That is a nice squad, quite adaptable.
The local play scene is quiet at the moment - mostly we play Dynamic Duos format so meta squads aren't as much a problem - people play for fun as an updated variant of the Epic Duels boardgame.
Imperial Assault plays more like Tannhauser, so its a different mindset being a hybrid rpg etc.

Though I digress, circling back to SWMinis;
CE's and Disrupt are also increasingly factors, because these change how pieces must move on a battle map.
So, some CE's cause an advantage to a scissors-paper-rock, but at the cost of exposure to AoE and direct damage abilities.
Maps are important because of different choke points and where Gambit is located, leading to potentially counterintuitive outcomes when looking at squad compositions.
Movement is a very important part of the game, especially for things like Attack of Opportunity.

Bump because it took me so long to go back in the scroll and find this thread. I just edited the main post to add a brief section about CEs and FPs.

I went looking for this thread to think about the Roger Stone Daala squad in this context.
http://www.bloomilk.com/Squad/178577/-roger-stone-of-swm-v2--2017-gencon-champion

Roger Stone Daala's categorization:

*OFFENSE: all of its damage through nonmelee attacks
*DEFENSE: Stealth on the Scouts and Diplomats (which weren't categorized above, but are most effective vs Melee)
*TANK/OVERWHELMING/TRADITIONAL-ATTACK: This squad is all traditional attacks.
*ROCK/PAPER/SCISSORS: This counts as paper. There's no big beatstick to go after and there's no scissors piece. There are 12 different pieces that can do damage. Two of them are 50 hit points, so it's maybe posterboard if you prefer, but paper is the bestcategorization.
*COMMANDER EFFECTS: This squad is very CE dependent and brings no CE suppression.
*FORCE POWERS: This squad has no Force powers and brings Force suppression.

So in theory it's weaknesses should be:

*OFFENSE: Against a balanced defense (Stealthy and possibly Super-Stealthy Scouts, Vulnerable Raxus, Diplomats for Melee), you can pick either melee or nonmelee or a mix and be okay. Just make sure you have a way to clear out Diplomats, and if you're shooting have a way to ignore cover for the Super-Stealthy Scouts.

*DEFENSE: Bring anti-shooter defense. Evade is helpful but with their long range, they base enemies easily, so it's probably not enough.

*TANK/OVERWHELMING/TRADITIONAL-ATTACK: Bring not just a little bit of anti-shooter defense, but a tank.

*ROCK/PAPER/SCISSORS: Against that paper squad, bring scissors.

*COMMANDER EFFECTS: Bring CE suppression and feel free to bring your own CEs.

*FORCE POWERS: Avoid bringing Force powers and no need to bring your own Force suppression.

The offense type doesn't matter much, but if you bring super-anti-shooter-tank with scissors capabilities, CE suppression, and a way to clear diplomats (that isn't a Force power), that theoretically should be an advantage.

Here's a squad that meets most of that criteria:
http://www.bloomilk.com/Squad/223102/

None of this addresses activations and movement. Those are good things in any squad, and Roger Stone Daala does those very well. The counter-squad will have to at least have some decent movement and activations, but should be okay without actually matching Roger Stone Daala.

This squad can tank and advance. Cloaked Disruptive so you can't get close and keep CEs, and you can't just come in and erase the Disruptive because it would require CEs to do it in one round. Soresu and RDE+4 means the Imperials hit at most 30% of their shots if they stay back (fewer than that after FPRR). The twins Leap past the Diplomat wall if Momaw doesn't War Throat it first. R2+Yobuck has greater range (38squares) than the Sled (24squares). Or maybe Daala wins easily.