Story is an upgrade over adventure 1, being much more complex and eventful. It even has a few twists here and there. Those twists aren't very good, but hey, it's a start. Shadow is a fan favorite character for a reason although I do wish that they hadn't retconned the ending. Rouge and Knuckles are both pretty unlikable in this game, Amy still has no reason to be here and is insufferable, Eggman is uncharacteristically threatening and serious (which is both a good and bad thing tbh), and Tails is a dumbass. Overall I don't like the cast aside from Shadow, who is really good, and I don't like the story aside from the ARK lore.
Sonic/Shadow: Universally considered the best part of the game and it's obvious why. While some stages can be a little too linear for my liking, most speed stages in the game make decent use of the physics, feature plenty of speed and platforming in equal parts, and a few different possible routes to take that generally follow sonic level design philosophy. Towards the end of the game though I feel as if they become a little too ambitious. The gravity gimmicks of Crazy Gadget and Final Chase are very intrusive and in the latter case, janky. Pyramid Cave is very boring, and Final Rush's grind rails aren't too fun to navigate for various reasons. Sometimes the camera won't give you a good view of the rail ending, sometimes trying to switch rails will fling you off into oblivion, and some rails just outright lead to your death. Before those levels though, these are a great time, and a massive improvement over the SA1 formula.
Tails/Eggman: Slower and clunkier version of SA1's Gamma. One of the things that made Gamma relatively fun for me was that I enjoyed shooting things while moving, trying to target as much as I could without stopping. SA2's version abandons this philosophy and requires frequent waiting, particularly in Tails' stages. Even though the two control the same, I swear that Eggman and Tails had different level designers because Tails' stages are PACKED with bullshit that Eggman just doesn't really have to deal with. Overall, most of these levels range from bad to mediocre, with the only ones that really stand out to me as good being Iron Gate and Cosmic Wall (both Eggman levels, go figure).
Knuckles/Rouge: While these two are as nimble as they should be physics wise, I have always hated the way they animate in this game. Level design wise, their stages are surprisingly challenging and built around their gliding moveset, which makes them more fun and interactive than their SA1 counterpart... on paper. But yeah, I'm gonna have to echo what everyone else has bashed about this game and say that the radar only tracking one item at a time is really stupid, and particularly annoying in the later, larger levels. Aquatic Mine and Death Chamber are disjointed, nightmarish mazes, and Mad Space... Mad... Space...
Lastly bosses in this game are pretty terrible. Fights against other playable characters are pathetic as always, and the other fights are pretty similar to each other. Only exceptions being Biolizard and Finalhazard. Biolizard is a Sonic Superstars tier disaster of a boss that is shockingly difficult to evade and relies on the unreliable homing attack to work. Every time I died to Biolizard it didn't feel like my fault.
The Finalhazard is even worse. The swapping between Sonic and Shadow idea is kinda cool on paper but functionally just takes away the balancing act that super forms have always presented: dealing damage but collecting enough rings to stay alive. Instead, your ring count is just a flat time limit. Furthermore, you're supposed to charge into the pink swelling spots on the Finalhazard to deal damage, but I SWEAR it only works when it wants to. Sometimes it just doesn't do damage and knocks me back instead. Again, it never feels like my fault when I die to this boss, which sucks cuz Perfect Chaos was a pretty fun final boss in SA1.
So yeah overall it's an upgrade over its prequel but still a heavily flawed and overrated game.