Display size on an OLED is not the determining factor, it's # of Pixels, and they're roughly the same. Pixels are turned on and off, not the whole display. But more important to battery life, is display efficiency (Samsung is the master of this, possibly the master's god), kernel efficiency and processing/resource management. Both LG and Samsung suck at the latter, but the Note series has traditionally done very well at prolonging battery life to tweaks to the kernel. If I was a betting man, my money would be on the Note 8 not just winning on battery life, but blowing LG out of the water.