Lots to like
I'm coming from an S4.
On the G3, I'm a big fan of the tap to wake/sleep functions. The screen looks sharp and bright to me. The 5.5" screen makes web browsing easier and games more fun. Video is more watchable too.
The G3 is bigger and it's heavier than the S4. It definitely feels like a bigger device. I'm still getting used to holding it and 1 hand operation is not quite as easy. The larger screen is definitely worth it though.
Sound, through the speaker, is loud enough, but not quite as clear as the S4 IMO. I plan to do some sound mods, so my opinion may change after mod.
Battery life is very good. I can easily get through my average day with juice to spare. I did kill most of the bloatware and I'm running stuff to kill background apps.
Current: Verizon LG G3, Galaxy Tab Pro 12.2 (SM-T900), Verizon Galaxy S4, Nexus 7, Nook Tablet
Past: Thunderbolt, Droid Incredible, Galaxy Nexus