Galaxy Nexus. and here's why:
-Jelly Bean has closed the gap as far as performance is concerned. It takes a phone that is almost a year old and puts it right in the mix again. I've got both right next to each other right now and I honestly think the Nexus is faster when it comes to scrolling through the UI. Probably helps that it doesn't have a launcher on top of it.
-Google Voice Search and Google Now are cooler than anything that's offered on the S3. S Voice can't compete with Google Voice Search whatsoever. I find myself using it all the time now and it directly ties into Google Now. What is normally just a gimmick on the iPhone and the S3 is extremely usable and useful on the Nexus.
-The notification shade is just awesome. They've taken things to another level here. Again, another useful thing you just can't get on the S3.
-It's stock Android. Beautifully designed UI that was so awesome before, but is even better now because of how responsive it is.
-The Jelly Bean keyboard is better than SwiftKey. It's on-par with the iPhone now.
-I think you're on T-Mobile, so you could order the unlocked Nexus that won't be restricted for updates by your carrier. Probably the biggest advantage the Nexus has over any other Android phone.
-It's still the Samsung Galaxy Nexus, which was a great phone from the start. It's subjective, but I like the build quality of the Nexus better than the S3.
For me, it was a no-brainer. I ordered the Nexus from Google only 4 days after I got the S3. The S3 does have a slightly better screen, more RAM, a faster CPU/GPU, and a better camera. The RAM and CPU/GPU advantage are hardly noticable when the Nexus is running Jelly Bean. The camera is still superior, but I kind of like the Nexus camera app better. Either way you go, you're going to have a great phone. If you have to choose, though, go with the Nexus.