I was very skeptical which was why I went for the Note first, but the Nexus is really the best smartphone I've ever used. If you care about customization then this is the device to go with, but if you don't mind using the interface that manufacturer/carriers give you, then go with the SIII. I just love how open the Nexus is, so easy to root and customize. If you have not use lots of custom roms before, this device seems very bare and light, but that is the advantage.
I bought the Nexus immediately after the SIII was announced because I didn't felt it was a major upgrade and the Nexus was going for $300 less. The most intensive thing I'll be doing is watch HD 1080p and the Nexus does it smoother than the Note. I feel buying the SIII would be a step backward to the freedom the Nexus provided. It's not pentaband, so I would have to wait for T-Mobile version to use their 3G. My family uses ATT so I can always hand the Nexus to them and not have to worry about 3G compatibilities. Though I heard T-Mobile SIII will support ATT 3G bands. In addition, the American version will be using proprietary Qualcomm CPU and GPU, I would have to wait longer for CM9 and AOKP roms and who knows if the development will be good as international version, which Samsung already released the source code for.
There is a major flaw with Nexus which is lacking microSD slot. Also the SIII use the same Sony camera sensor as iPhone 4S so it will take better photos and have fast shutter like the Nexus.
I'm keeping my eyes on the SIII, but I want to wait till there are lots of stable roms for the T-Mobile version and if the price go down enough by end of year holidays. Right now I rather wait for the next Nexus phone. It seems like a good phone, but isn't ground breaking like the SII was, especially in term of durability like some youtube drop test has shown.