BIG improvement over Sonic 1. Better game play, and the introduction to my favorite Sonic character: Tails!
Alright, now that I got that out of the way:
Game play: 9/10
Sonic 2 plays with the same premise as the first one. Get to the end of each level collecting as many rings as you can, and then defeating the boss is the last Act of each level. While trying this, you can try to get all of the Chaos Emeralds. Although collecting all of the Chaos Emeralds is a little bit easier this time, it's still really hard to pull off, so I wouldn't suggest trying too hard to collect all of them if you're looking to have a more fun time. If you want all of them without going through all the trouble, use the in-game cheat to get them all.
Anyway, Sonic 2 is a whole lot easier than the first game, making it less frustrating for younger players. This makes Sonic 1 one of the more "hardcore" Sonic games, since it's actually quite a difficult game. Simply put: Sonic 2 is easier than Sonic 1. Here's some proof to sort of back this up:
Okay, in the first Sonic game, there were three "Acts" in each "Zone". There were six Zones in all. In Sonic 2, however, there are only TWO Acts in each Zone, with the exception of the last four Zones which have three or one Act(s). There are eleven Zones, so Sonic 2 might seem longer than Sonic 1. But due to the difficulty level of Sonic 1, Sonic 1 might actually take a lot longer to beat than Sonic 2.
Another reason why Sonic 2 is easier is because the levels themselves are pretty easy. The new "Spin Dash" makes the method of running back a little strip of land in order to run across it again to get some speed totally obsolete. Now, you can instantly make a burst of speed by simply holding down, pressing A or B a couple times, then releasing the buttons. This makes certain parts of the already easy levels easier. Also, as mentioned earlier, getting the Chaos Emeralds is still hard in Sonic 2, but getting to the special stages to collect these Emeralds is much easier this time. Instead of having fifty rings when reaching the goal and jumping into a giant ring, you only have to have fifty rings when touching a save post, then jumping into a ring of stars above the save post. Once you're done with the special stage, you lose all of the rings you had. This may be a way to stop you from easily getting to another special stage so easily. But this can be avoided to some extent by backtracking though the Act and collecting rings again, because entering a special stage resets all of the rings in the Act, so you can go and get fifty rings again, then reach a different save post and enter the special stage again a second time. There are usually around three save posts in each Act, so if you're really good, you can get every Chaos Emerald in only two Acts! The Sonic 2 special stages are easier than the Sonic 1 special stages, but not by very much. Instead of jumping through awkward, rotating areas, you're running down a chute, collecting the desired amount of rings. The only really easy special stage level is the first one. The second, third, and all the other ones are darn near impossible. Kind of.
Anyway, another way Sonic 2 is easier than Sonic 1 are the boss fights with Dr. Robotnik. A lot of his battle strategies leave him wide open for attack for long periods of time, and since you can have the second player play as invincible Tails, you can pretty much beat him in only a few seconds in most cases. The final boss is a little harder than the final boss in Sonic 1 (which is EASY), though.
Controls: 9/10
The same as Sonic 1, only with the added spin dash.
Graphics: 10/10
The graphics are on par with the first one's, but probably a little more bright and colorful. Very vibrant.
Music: 10/10
The music in Sonic 2 is a lot more memorable and upbeat than the first.
Overall, I recommend Sonic 2 over Sonic 1. It's more fun, in my opinion.