For those not in the know, I will explain those two points.
First, the bosses, because that's easier to explain.
In Sonic Advance 1 and 3, you have pretty standard boss fights. You can move about as you like.
In Sonic Advance 2, you're constantly running after the boss, so it's a bit more difficult to move as you want. I honestly don't mind it that much, but it is still an inferior way of doing it and a lot of people didn't like it.
In Sonic Advance 1, all you had to do was find the special spring. I think there was one per zone (not act, zone), so it could be pretty difficult to find it, but once you know where it is, it's just a case of restarting the stage if you fail it. The Special Stages are... questionable though. It's an odd 3D sort of thing and... can be hard to judge depth and whatnot and where the rings ACTUALLY are.
In Sonic Advance 2, there are 7 SP Rings scattered in every act. And you have to collect all 7 of them without dying. And, uh... yeah, for some of the stages, that is a huge pain in the ass. It is made even worse in that you can't just farm the same stage to get them all, each Zone has a different coloured Emerald. The special stages themselves are a 3D plane with lots of rings and Zero from Sonic Adventure 1 chasing you. Collect 300 rings and the Emerald is yours. It is made easier by there being combos if you collect a lot of rings in a row, and it is actually necessary to do this, because there is not 300 rings in the Special Stage.
In Sonic Advance 3, there are Chao scattered amongst the stages, 10 in each Zone. They can be anywhere in Acts 1-3 of each Stage, or the Hub area. Once you collect a Chao though, it is collected permanently, so you don't need to keep doing it. Once you have all the Chao in one zone, you can find keys. Exiting or finishing the stage gives you that Key. You can stockpile up to 9 at a time, and it takes one key to enter the Special Stage. Which is kinda similar to the Sonic Advance 1 special stages, except rather than being on a board, you're on the Tornado's wing. Collect enough rings and a Chaos Emerald is yours. Again, one per Zone.