I've used both the GNEX and the S3. My opinion is that the S3 is moderately better than the GNEX, but not a huge game-changer.
I agree with most of the points above, but should say the following:
1. I actually think the GNEX form factor is nicer than the S3. The dimpled back is easy to grip and it has more heft and solidity.
2. I hate Touchwiz. It is wildly different than AOSP (think email, messaging, typing, calling, etc.) I am running Carbon rom for the AOSP feel, but it's far from perfect.
That said, the S3 is much faster and has what seems like quadruple the battery life, better screen, and better call quality. These things are much more important. And, so on balance, I say the S3 is moderately better than the GNEX.