Sonic 2 is the perfect example of looking at a flawed product (Sonic 1) and knowing exactly what needed to be fixed.
All of the pieces are the same, but refined. Level design that allows for more instances of feeling like you're actually going fast. Way less death pits. A less punishing special stage and an actual reward for completing them all. Tails, another 10/10 character design (even if he can be a hindrance rather than a help sometimes). An overall visual upgrade. Better boss designs (and an actual climatic final boss). Sonic 2 is the game that Sonic 1 should have been.
If there's any fault to be found, it's that the actual 2 player mode is a little undercooked, and some people might take issue with the difficulty curve. The game is fairly easy most of the way through, then spikes hard near the end. It's a game that rewards speed and precision platforming, but doesn't necessarily punish you for failing until near the end of the game.
Sonic 2 to me was the pinnacle of this formula they stumbled upon. While the games would get more bombastic, they started to lose the simplicity of what Sonic was. There's next to no story, almost zero cutscenes, just you and a desire to go fast.