It's faster. Screens slide smoother, apps launch quicker and stuff just works better. But that shouldn't really come as a surprise — we've seen the difference between an A4 and an A5 processor before. What IS surprising is just how fast the 4S' camera is. That thing KILLS.
We tested the iPhone 4S against the iPhone 4 and iPad 2 and though the 4S felt better when compared to the iPhone 4, it's not an iPad 2/iPad 1-sized difference where you feel like the old generation is incredibly slow and it's impossible to ever go back. However! It'd be foolish to discredit the speed difference because it clearly exists and it definitely improves the iOS app-launchy, screen-slidey experience. iOS is just slicker on the 4S, things work better and you get to do what you want to do faster.
Where the iPhone 4S truly blows the iPhone 4 away is in its camera speed. I tried to "rapid fire" the cameras in both devices — obviously more of a stress test than a real-world test — and the results were stunning. First, the iPhone 4 camera takes MUCH longer than the 4S camera to open. And then when I started taking pictures over and over and over again, the iPhone 4S handled it with ease. Saying the camera in the iPhone 4 struggled is a bit of an understatement; in a solid 10-15 seconds of button mashing, the iPhone 4S managed to take twice as many photos as its predecessor. The camera speed in the 4S is legit, folks.
The iPhone 4S also shines in more intensive games like Infinity Blade and NBA Jam. The iPhone 4 isn't even on the same level, actually, sword swipes swoop smoother and controls feel more responsive on the 4S. What we saw in our testing was the iPhone 4S and iPad 2 battling it out for first place while the old iPhone wasn't even close. And that's the real gist of it, the iPhone 4S compares more to the iPad 2 than the old iPhone 4. And that's a pretty good place to be.