I honestly think they could make any terrible Sonic game they wanted but as long as they added the Chao Garden and animals inside the stages, the fans would love it without question. Not that I would want them to do that, I'd rather they at least try to make a decent game then add the system back in.
I have yet to play Generations so I don't know how good it is yet, from what I've seen it looks like a simple remake to try out the old Sega Genesis Sonic and the more recent Sonic Colors Sonic. I honestly didn't enjoy Sonic Colors that much.
What I love about Adventure and missed in Adventure 2 was the free-roaming exploration of Station Square/Mystic Ruins/Egg Carrier. But the one thing they both shared was that although you were required to get from point A to point B in stages, you didn't have to run forward exactly. You were free to walk around the stages and screw about if you wanted. The games seem to be more about going in one direction these days, with little exploration.
The chao system was pretty much the same in both games, with a few noticeable differences. There is a lot they could do with it these days, and it would be nice if they finally did something. It would be nice if they could at least explain why they have not done a Chao Garden in such a long time too.
A few things they could do would be a better evolving system, where the Chao's character model would evolve as it was feed/given animals, among other things. They could add online capabilities where you could go to other gardens, or race your friends Chao and whatnot. That's just off the top of my head, but they could do so much more if they tried.