The second game in the series made some changes to the formula. In the original game, each Zone had 3 acts, but now there's 2 acts (up until the final part of the game), but you get more Zones for extra variety.
Sonic also has a sidekick in this game; a two-tailed fox named Tails who constantly follows you around. Tails generally makes a fool of himself, being hit by enemies, falling off platforms, and generally lagging behind. On a positive note, he doesn't cause any negative effects, other than the visual annoyance, but can be a help in collecting rings and even chipping in the occasional attack on the boss.
The levels are even bigger, with more alternative routes to take. Longer levels means that the rings are more plentiful, giving more scope for the extra lives. Another change is that if you pass a checkpoint with 50 rings, you have immediate access to the bonus stage, rather than having to finish the level.
The levels contain various levels of elevation and require Sonic to travel vertically as well as horizontally. Despite people believing Sonic is all about speed, the original game was more about momentum and careful control; given that there were plenty of dangers and plenty of objects that prevent you from going fast. The level design in this sequel gives Sonic more scope for picking up speed. Also, a spin dash move is also available which can be charged by crouching and holding jump. This means you no longer need to back-track to take a run-up to overcome loops and ramps, meaning that momentum is no longer as important.
In the original game, you had to complete the game in one sitting and with a limited amount of lives. This meant you had to repeatedly replay the game in order to build up enough skill and learn the levels. It can be very frustrating to play at times due to parts of the level design eg spikes that appear out of nowhere, poor enemy placement etc. The game really is about learning the game mechanics; the level design, enemies, and pacing. Modern versions of the game (like Sonic Mega Collection which I played), you can save at any point, which helps relieve some of the frustrating elements.
Metropolis Zone in particular has some really frustrating enemy placements, like when you land a jump, a praying mantis (Slicer) or the equally annoying crab (Shellcraker) whacks you. There's also some lovely exploding starfish (Asteron) that knock you off your rotating screw, and you are forced to backtrack a certain distance to get the screw to reset. The penultimate level, Sky Chase has Sonic standing on top of Tails' plane. You can move around as well as jump, and Tails will always keep you on the plane, but it is so slow and boring. The turtles look way out of place in the sky, since they just remain stationary, but there again, the entire level is out of place. Then when the next level starts, it seems to show a cutscene but you are expected to jump off the plane and onto Robotniks airship within a 2 second time-frame. If you don't; then you die. Wing Fortress Zone is not too fun either and it's often not very obvious where you need to go. There's also some strangely placed platforms and Sonic has to jump on them from hanging on a bar, but there's no animation and he falls strangely; making it even harder to land. When you do reach the end, you are expected to defeat two bosses with no rings which is quite a challenge. You have to work out what damages you and what doesn't but there seems little margin for error, and taking damage is instant death which is an extreme penalty.
Overall, I felt the larger levels made for a positive improvement, bringing an increased pace as well as the added variety. Despite having some use, Tails seems like an annoying addition, and could have been implemented better. Although the game seems potentially better than Sonic 1 early on, I didn't enjoy the final set of sections at all which tainted the overall experience.