I own both the Nexus 4, personal phone, and the LG G2, my current work phone.
Personally, the screen on the G2 is just a tad to large... honestly, holding the phone in your right hand you cannot comfortably touch the top left area of the screen without shifting your grip or using your other hand, and I have fairly large hands. That is my only complaint about the G2 compared to the N4, other than that the G2 is amazing. I have the Verizon version, all the bloat (around 9GB of it) killed me though, less than 48 hours and I had it running Beanstalk ROM.
If battery life is important, the G2 has stellar performance there, truly amazing... 4-5 hours screen time in a day and still have 50% battery, something my N4 could not do.
If romming is your thing, then the G2 isn't quite as forgiving as the N4... I have both phones rooted and running Beanstalk, the N4 is rock solid smooth, never had a single issue, the G2 has given me 2 SoD and 2 random reboots in the last 3 weeks.
If you have any specific questions about the differences , just ask, I use both on a daily basis... I'll be glad to answer any questions.