I am on TMobile and I do have both phones. So using your list of priorities on a phone:
battery life
screen brightness are the most important
I would say both are very good on the battery life.
I know there have been some posters that have had issues with battery life on the LG (and the N6), but I haven't seen any major issues. To me, both are equally good during the day. Both should give you at least 12 hrs of battery life.
As far as screen
LG G4- 5.5-inch Quad HD IPS Quantum Display (2560 x 1440, 538ppi)
Nexus 6 - 5.96" 2560 x 1440 QHD AMOLED display (493 ppi)
At least to my eyes, I find the N6 brighter than the LG G4.
followed by camera and stock Android or close to it.
Camera on the LG G4 is far superior than the N6. Personally, the interface is a bit wonky on the N6 and the images that come out are a tad inferior than from what I was getting with the Samsung S6 or now with the LG G4.
As far as stock Android...well...N6. Obviously. There are other manufacturers that do have close to stock Android, but neither LG 4 or Samsung S6. You either love LG G4 take on Lollipop Android...or you don't.