What you wrote makes little sense. The Nexus 4 and Note 2 have nearly the same pixel dimensions. The Nexus 4 has only 48 more pixels in length but as far as height it is robbed of pixels because of the on-screen nav buttons (which I grew to abhor).
That doesn't even take into account the fact that the Note 2's screen is so much larger, physically.
I currently have both a Note 2 and Nexus 4 and while I like the Nexus I would never choose it over my Note 2 due to screen (and certainly not battery life). What I like about the Nexus is that it is pure Android and not contaminated by a carrier and/or manufacture. (That said I am not disliking touchwiz.)
There are ways to get the full screen back for Nexus 4, through custom ROMs (ParanoidAndroid is the one I'm referring to), but of course that requires you to install custom ROMs, which I guess some people might be scared to try.