The GSIII is a faster phone with a bigger screen, twice the RAM a better camera (8MP). It also has a microSD slot to add more user storage, whereas the GNex phones do not. By default, the GSIII will have Samsung's TouchWiz UI; the GNex is pure Android, with the stock Google UI.
The unlocked GSM GNex will get faster software upgrades than the Sprint and Verizon variants, because they push directly from Google, whereas the carrier locked versions update via the carriers. The carrier locked variants will also have some carrier software preinstalled on them. Those are a couple of things to consider.
I played with both the GNex and the GSIII at the Sprint store to get a feel for both phones. While the GSIII is indeed a snappier device, the GNex is no slouch by any stretch. I actually like the GNex better because it's a little easier to use single-handed (the GSIII is a very BIG phone) and the minor differences in hardware are hard to justify for the price difference, at least to me.
Ultimately, I think I'm going to order the unlocked GSM GNex from straight from Google next week and activate it on T-Mobile. It's hard to pass up for $349, and I'm not exactly thrilled about signing another 2-year agreement with Sprint, when the future of LTE deployment in Phoenix is uncertain.