GS3
Access to LTE, Touchwiz adds some cool features, expandable storage and battery access. You can replace the touchwiz launcher with Holo HD if you want a stock android look or you can flash an AOSP rom if capable.
The Nexus 4 competes on price but when it is hard to get a hold of (Till mid Feb) and when you can get a GS3 similarly priced why lean towards the Nexus 4.
My 4S doesn't have LTE and it isn't all that big a deal to me for this phone.
I currently sit at about 2 GB used on my work iPhone - absolutely no need for expandable storage.
If the battery works, I would have no need to replace it - I won't be buying backup batteries as I won't be using the phone heavily.
The main draw to vanilla Android for me isn't so much the look as it is the timely updates and longevity of said updates.
Plus, I'm not in a place to buy now so availability isn't a huge concern (yet).
The reasons the GS3 has entered the conversation are mainly due to TouchWiz's features and the ergonomics of the phone itself.
I have to say though, I'm leaning more towards the Nexus 4.