Why the heroes were the most unbalanced thing in the game
The following were severe issues with the heroes:
1. There are too many abilities that had the potential to 1-hit infantry - some in the list below can even do this to heavies.
Let's cut to the chase. Anakin's passionate strike, Grievous' thrust surge, Han's detonite charge, Chewie's slam, Iden's alt fire, both pushes from Luke and Obi-Wan, Dooku's duelist, BB'8's rolling charge... okay, there are a lot of them. Take my word for it.
The bottom line is that this means heroes are sooo OP against infantry. Yes infantry should be weaker, but when they can be 1-hit by practically half the abilities in the game, they really do stand no chance whatsoever. The above abilities needed to be nerfed to not 1-hit infantry - and in the case of Chewie's slam, Han's detonite and especially Anakin's passionate strike, these can 1-hit heavies. Not balanced in my opinion.
2. Saber heroes could spam blaster heroes with no repercussions, yet blaster heroes cannot do the same back.
This all comes down to one thing: stun.
Whenever a blaster hero gets hit by a saber, they get stun and this stops them from being able to fight properly. But whenever a saber hero gets hit by a blaster bolt, they can freely keep swinging. This doesn't help considering saber swing speed is pretty obscene in most cases (looking especially at Luke, Dooku, Vader and Maul for this one). So, when saber heroes get hit by a blaster bolt, they should also be stunned. This would still leave saber heroes stronger due to their block but it would balance it a bit at least.
3. Anakin's passionate strike
One of the most unbalanced abilities in the game - not only does it cut through a block (an immediate no-no) it can follow you if you run or dodge, making it a bit pointless to even try. Furthermore it deals enough damage against troopers to 1-hit heavies. Yes Anakin is left vulnerable for a split second, and if you're good you can get in a hit, but if you spam you can attack almost immediately after it is over, and if you hold block your block will go up almost as soon as it is over.
4. Iden's alt fire
Iden's alt fire is a block breaker that deals 150 damage for a not-even quite direct hit, and can be fired very frequently, killing every hero very fast. And they can't block it at all. Very OP in my opinion, especially against blasters who can't force jump out of the way.
5. Saber hero blocking stamina vs. blasters
It's ridiculous, in all honesty. Saber heroes can deflect 1000+ damage of blasters with ease, and some (Vader, Anakin, Obi-Wan) can even do it with very good accuracy. This can melt through a blaster hero's health before they know it. I know about the Rogue One hallway scene, but it would be OP if Vader could do that in-game... oh wait, he basically can. (We'll get onto Vader in general later). So it is very very OP. They needed to reduce saber heroes' blocking stamina vs blasters by about half for every hero.
6. Stuns and ragdolls
Some of these points are worse than others: stun is a particularly bad one. Not only does it happen to blaster heroes when they get hit, there are many abilities that stun or ragdoll in the game, being both droids from Phasma and Iden, Chewie's grenade, Luke's push and repulse, Anakin's heroic might, pull and retribution, Dooku's lightning... ok, there are way too many of them. Plus you're hopeless whilst being ragdolled and you can't swing, shoot or block. Stun in lightsaber duels is another thing - it can immobilize you for so long that you can't use your abilities for about 1 and a half seconds and then you die.
7. Saber swing speed and damage
This is something that wasn't an issue until later in the game's life cycle. But once they added Grievous, decided to make Luke Mr Whizz, buffed Dooku's duelist and increased everyone's damage into the 120-140 range, things got really unbalanced. Saber DPS is stupid and ridiculous compared to blaster DPS - especially considering no-one hits every shot. Couple this with the stun blaster heroes get when hit, and you have a very overpowered combo.
Look at how fast Yoda and Anakin can hit - everyone should hit about like them. Dooku, Vader, Rey etc all hit way too fast. It's really unbalanced.
8. BB-9E
Need I say very much? He can stun every 4 seconds which is very frequently indeed (ridiculous and very annoying) and has a ragdoll ability he can use to regen, then rinse and repeat with the stun. Super annoying.
9. Count Dooku
He can literally kill Yoda in 2 swings with the right star cards from behind - 392+342 damage is 734 damage which means he can kill most heroes in 2 swings. Admittedly you do need star cards for this, but consider that Dooku literally has the fastest swing in the game with duelist and expose weakness stops your movement, then it is much too powerful.
10. Dooku/Luke stamina cards
These grant 35% attack and block stamina instantly compared with Rey who can only gain 10% swing stamina only, and Kylo and Yoda who don't even gain 25% swing stamina and no block stamina. At least you have to build up Obi-Wan's and Anakin's making them more balanced.
11. Darth Vader
This dude is arguably more powerful than launch Anakin - the way he is made means you can use an incredibly cheesy playstyle of waiting for someone to attack, parrying with the choke, getting an aerial swing and then a saber throw + swing if you're good. Then you can just backdodge, block and parry until choke comes back. Cheesy as hell. Not to mention the fact that his glide makes hookswings VERY easy to land compared to all the other saber heroes. And then you have the bonus health + furious resilience combo which all in all amounts to about 1400 health. Not to mention focused rage gives him bonus damage and double the stamina. And then there's fueling the rage - which only sacrifices 5 damage/swing for an extra 6 seconds of double stamina and potential 25% DR if you have furious resilience. It is too powerful for sure.
Well, that is not an exhaustive list, I'm sure there are more. I hope you agree with my points, and if you know any more points, can you let me know in the comments?
The heroes and villains have always been more powerful than the troopers. This makes sense since that's the way it is in the Star Wars universe. How much so is obviously up for debate, as you've indicated.