Here is a list for the best games that run only on iPhone 4S. They may run on the iPhone 4 but in most cases, they aren't going to run like the iPhone 4S would.
Galaxy On Fire 2: This game has been known to have outstanding graphics and some of the most awesome explosions! These graphics have been updated to an unreal amount of detail, you could compare this to the Wii graphics, this will win. You do need an iPhone 4S to experience these graphics.
Epic Citadel: Epic Games sure went all out on this app. This is not really a game, more of an exploration or tech demo to show off the Unreal Engine technology that is now on a mobile devices! The Unreal Engine was used in many of the best games on Xbox360 and PC such as Gears of War and Unreal Tournament. This will be a little laggy on the iPhone 4 that's why I say this game is made for the iPhone 4S.
Infinity Blade 2: Infinity Blade 1 took everyone by storm. Sold over 1 million apps in the first month and grossed about 20 million dollars in 8 months. There was was no doubt in their minds that a second Infinity Blade had to be created. Infinity Blade 2 was released, winning the award for best mobile game of the year, also winning the best visuals award. Most people say this game has the best graphics that ever appeared on a mobile device. I believe its true. You can compare this too PlayStation 2 games or early Xbox 360 games. This was demoed at WWDC on the iPhone 4S and looked much better than the iPhone 4.
Carve The Copper Relief: Phyzios is known for making alot of little fun games. They specialize in physics, they created Phyzios studio on the PC which was a physics tool that was really fun to use, but a few months ago, Phyzios decided to shut down their PC apps and website to move on with iPhone and iPad apps. They broke out with a huge success on Battleship Craft on iPhone and iPad. They released a ton of apps since then, but what I'm most interested in is "Carve The Copper Relief". I had this app on both iPhone 4 and iPhone 4S. as simple as this app looks, it is highly advanced. On the iPhone 4 this apps is almost unusable. It will lag ever second or either crash on you. On the iPhone 4S it ran perfectly smooth, no issues.