Nexus 4 or iPhone 5?

Unfortunately, my iPhone 4's battery is starting to get crappier every day (started shutting down at 10%, then 20, 30, and now 50%), so I can't wait around for a possible Nexus phone with LTE.

Both the iPhone 5 and Nexus 4 look really appealing to me, but the reasons I'm split are that:

1) I don't necessarily want to be stuck in another two year contract

2) I much prefer Android OS, but I have a Nexus 7, so being split between the two wouldn't be so bad (assuming iOS 7.0 actually catches up to Android)

3) The iPhone 5 has LTE (which is ubiquitous and fast in my area), and I'm grandfathered into unlimited data through AT&T which I really wouldn't want to give up by moving to T-mobile. Yet, I'm not sure LTE will really be that important since I have decent internet at home, work, and school.

4) The screen size of the iPhone 4 really doesn't bother me, but I would probably be happier with the larger screen of the Nexus 4.

So I guess it boils down to, should I squander the unlimited LTE or stay with an OS that I don't really like as much?