would depend on what you want your phone to do, going from S3 to nexus 4 you sacrifice removable battery and ext sd card for quicker updates and 2gb ram so not much between them. With both id be waiting till Note 3 is announced next month as prices should tumble on Note2 but it would be my pick if you didn't mind the bigger screen.
XT is a Dual Carrier network - but it all comes down to what you're doing on your phone. DC HSDPA is faster but you won't notice it if you're just doing Facebook, Twitter or light tasks on your phone. Personally, I don't think you'll notice much difference between the Note 2 and the DC version in real world tests unless if you're doing speedtests.
The Nexus 4 is extremely good and was one of my more favourable phones I have owned. Again, comes down to what you're wanting to do, both are excellent devices, might be worth even looking at the Galaxy S4 since for you it ticks all boxes and as-long as you don't liquid damage it then it's futureproofing you a bit more.
I think that you should take nexus 4. Better hardware, more support, and better OS. The only thing Note 2 is better than Nexus 4 is that has a longer battery life, and a slightly better camera. That's it. Note 2 has pixelated screen and is a very big device. I suggest you try them both if you have the chance, and make the decision.