Phone for College

Hey everyone!

So I'm going off to college in the fall to a big campus. My current phone, a Lumia 920, has served me well, but the battery has become awful, and I'll need a long lasting phone for school. So I've been researching bigger phones with bigger batteries, and I wanted to hear your opinion on which one you think would be best. Or, if your suggestion isn't listed, pitch it! I'm open to pretty much anything. Unlocked and below $400 is the best configuration.

My first choice is a Huawei Ascend Mate 2 LTE. With a massive 4050 mah battery with an equally massive 7.1 inch screen, this phone could potentially go for 2 straight days. The only downside is that its only 720p with midrange specs, and there aren't too many good review out there for it. Sells for $299 unlocked though! I'd also like to get off Windows phone if possible.

My next choice is a Sony Xperia Z Ultra LTE. Same concept, big phone with big battery. However, the specs on this are decidedly more high end, with a 1080p screen and such. Battery stands at ~3050 mah I believe, and Sony enhancements make the battery go farther. I could snatch one on Ebay for ~$360-$400.

The other choice is... a Nexus 5! I'd probably have to get a battery case though. Although the updates would be nice.

Please feel free to post your own options too! Thanks guys :)