The overworld gave out story elements and gave you a feel you were actually in the world. It was far better for getting upgrades, going to new places (and having hidden emblems to find in) than SA2's "get stuff while in the level" thing and the fact you just jumped around from place to place. In short there was actually nothing more to the game than just the levels, which was a downgrade from the SA style system where the overworld actually added to the game.
While they replaced 6 characters with 6 in SA2 and put the 3(4) most popular elements to both good and baddies, that is the fighting, shooting, hunting and racing. However I quite liked playing Tails as a runner, racing against Sonic, and it was probably my favourite mode. Amy's parts were quite annoying and Big's could be annoying, especially trying to catch the bigger fish, but you have to admit they broke up the action a bit and both of them offered a different playstyle (along with Tails) from just running around with Sonic. In SA2 both dark and good offered exactly the same playstyle and so it just felt like you were playing 3 characters with more levels and that's hardly what I call variety. Also the individual (end) boss battles in SA kicked major ***, which was in addition to a better final boss fight.
http://uk.youtube.com/watch?v=hZcysdmCJdk has to be the best out of them.
2 things primarily killed it for me. Shadow the Hedgehog, namely because he's
lame. He's just the stereotypical evil clone of Sonic, bla bla bla, and not only was he cliched and lame but he got a legion of stupid Sonic fanboys that humped him for being "cool". Oh yeah Rouge was pretty poor as well, but no-one likes her anyway. The other thing that killed it for me was the rankings. In SA it was enough just to pass what the stage asked you to do and you get your award, that's awesome. In SA2 however they felt the need to slap grades onto the whole ordeal and rather now than just passing what the thing simply wants you to do, you now have to pass it FASTER and WITH MORE RINGS and KILLING ALL THE ENEMIES etc. and that killed most of the fun out of it. I just prefered it when the challenge was the challenge itself and not "well, you did what we wanted you to do, but we're going to give you a C, come back and do it better". Oh and Sonic Heroes wasn't really a bad game, just flawed, and I'm sure it's better, although I haven't played it, than the abomination that is Shadow the Hedgehog.