You'll never know until you try them both for yourself. I spent two weeks with the Evo and took it back for the SIII. So far, LOVING the S3. In my experience, the camera is better, the software is faster and more fluid, there is less bloat, Touchwiz is ACTUALLY adding functionality to Android 4.0 rather than hindering it (I'm looking at you, HTC multitasking), GPS locks on faster, and the build quality is superior. That last point is entirely subjective, but after owning an Evo 3D for 3 months and having the metal frame bent in on the front, I wasn't going to risk it with the LTE (especially because it looks to be made from similar metals).
Battery life is also an improvement, and hey, even if it's not (which it is), there's an option for a second battery or even an extended battery. The phone charges nearly twice as fast as the Evo. The development on this phone is KILLER and to top it all off, you get an extra gig of ram. I keep hearing from evo users: "blargh, benchmarks! blargh!" It's been almost 3 years since benchmarks were taken seriously for a phone's day-to-day performance. They mean almost nothing these days. I also hear "Blargh, Sense > Touchwiz!" How? Why? Because of oversized widgets? Because it looks "prettier?" Sense does have some decent aesthetic cues here and there, but overall, Sense to me is like this overweight tank of a woman who wears too much makeup. EVERYTHING in Android 4.0 has been in one way or another "touched up" by Sense, for better or for worse (and usually for worse). Case in point:
Multitasking
Browser
Notification bar (no toggles, no percentage on stock)
Launcher (constantly reloads because it is a resource hog)
The friggin' ONSCREEN MENU BUTTON that takes up ~10% screen space on certain apps
Poorly designed physical buttons (Camera button is not really two-stage, sticky and recessed volume and power buttons)
Inconsistent/laggy transitions
The pro's are that you get a nicer screen, slightly better radios, a kickstand, and troll privileges on the S3 forums