Returning to Android after year long hiatus (with iPhone). Nexus 4 or SGSIII?

Smartphone history: HTC Magic, Nexus One, iPhone 4S.

Hey all, I realise it's going to be tough to call this one without the Nexus 4 being released yet. However we do know quite a bit about it, and we know everything about the SGSIII.

Long story short, I always liked Android. Last year when the iPhone 4S was released, and after having used an iPad (work) I decided to jump ship from a Nexus One (Cyanogen) to the iPhone 4S. I liked it. After a while I got bored/frustrated and jailbroke it. Now I'm bored and frustrated again. Also reminded of what I'm missing in Android land by my Nexus 7 (work), so I'm looking to sell the 4S and head back to Android.

Now my indecision begins. I'm immediately drawn to the Nexus 4 for obvious reasons - "pure" Android, and quick updates.
Also been looking at the SGSIII. It's a really nice phone, TouchWiz doesn't actually look bad any more, in fact it seems to offer some useful stuff (notification area toggles for settings in particular).

I can get a SIM free SGSIII 16GB for ~£400. A 16GB Nexus 4 is going to cost more than that (the 8GB is ~£390).

Any huge points I'm missing on why one would clearly be better than the other?