The better camera, SD card slot, bigger screen, and thinner design make the SIII a clear winner in my book. However, I'd take the S3 over the Nexus if it had NONE of those features. Why?
The processor. The Snapdragon S4 with its 28nm process and integrated LTE is a huge winner in my book. The enormous battery gains the S3 enjoys over the Nexus is too much to pass up. Couple that with the superior radio performance of the S3 in all areas (especially WiFi) versus the Nexus and there's no way I'd stay with my Nexus. The only reason I'd ever keep my Nexus over the S3 would be if the S3 were locked down, but since Samsung is awesome and doesn't lock its phones, I can enjoy all of the benefits of the S3 without having to necessarily give up stock Android.
Sure, I loathe Android skins and have written many rants over the past few years about how bad skins are, but touchwiz nature ux is among the least intrusive, in some ways is (kinda) handsome looking, and won't be on there long anyway once CM9 comes to the phone. I'm hoping for full-fledged CM9 support within 2 months of the release of the phone on Verizon (nightlies for the US version, with no major bugs such as radio or kernel issues).
We'll see if CM9 comes to fruition that soon, but even if not I can deal with Touchwiz. The problem with my Nexus (I'm on my 4th replacement) is the utterly terrible call reception and microphone performance during voice calls. Callers constantly complain that my voice sounds muffled or that it cuts out, a problem I did not have on my Thunderbolt, nor my Droid X or OG Droid.
Suffice it to say, the hardware advantages of the S3 are enormous, enough so that there's many clear reasons why I will be upgrading to the S3 and leaving my very beloved Galaxy Nexus behind. I believe the next generation of Nexus hardware will yield much better performance than the Galaxy Nexus, and I'll proudly return to being a Nexus owner if that is the case. For now, I trust Samsung to get it right with the S3.