Ok, just to make it clear, we're comparing the Heroes at their most powerful (ie towards the end of the game), without their full realized potential, solely on the attacks their know as-is.
This does mean that the question cannot be definitively answered for now due to incompleteness of TSoG, as the Hero may evolve, learn more powerful attacks, etc.
Under these criteria, the TPA2 Hero is the weakest, with only one type of elemental attacks, coupled with Feedback/Vengeance, and no shields. 6 attacks overall.
TPA1 is a mix-and-mash, he has 3 elemental blasts, knows two area attacks (Pyro Hail and Cryo CRoss), needs an orb to learn Vengeance or Big Shield, but has the basic Feedback and Vencgeance. 8 attacks overall.
TRPG1&2 Main knows the same as TPA2, but needs an orb to boost his Heat Powers, but posses the ability to use Shields. That makes the Main more powerful than TPA2, methinks. Also is limited to fewest attacks: 4 only. Overall, I'd say that ranks lower than the more multi-elemental TPA1 Hero.
TSoG: can learn up to 15 attacks, the most versatile array of shields available without orbs, can learn only one elemental attack (so far), which is the main questioning point, as upon learning attacks of one type, can go beyond any other Hero in the range of applications, including elemental shields (and the big shield version of elemental shields- something TPA2 Hero cannot do). Can also learn Vengence and Feedback without resorting to use of any orb. The only question hanging is over ability to use more than one element in attack: if he can, then he is the undisputed strongest Hero, if he can't, then TPA1 Hero has a pretty good chance as well- not as much depth in any of the areas, but versatility of elemental attacks is very impressive indeed.