I have owned the Note 3 as well as the Nexus 5 and went with the G2 in the end. The "gimmicks" in LGs ui are actually pretty useful for the most part and are integrated better than Samsung's in my opinion, especially after you ditch the stock theme. I never used a lot of them on the S4 or Note 3(with the exception of smart stay) but find myself using LG's add-ins more and finding them convenient and many times improving the experience. That said I should mention that I'm a true 1 handed user as I'm paralyzed in one arm. The Note 3 was just to big to use daily one handed and had minimal accessibility options to improve that. The G2 and Nexus 5 fit well in my hand and are pretty useable out of the box, the G2 is better for me tho because it does have a lot of accessibility options for more conveniently operating the device one handed.
As for the buttons on the back, at first I was worried also, but honestly I rarely use them. Knock on is one of those "dang this is awesome" kind of features and I'll want it or something similar in any future phone I own as it just flat out makes sense!
Additional info that swayed me, battery life on my Nexus 5 sucked! I live in a 1-2 bar area and it just drained the battery like crazy, the G2 seems to handle poor signal much better and I easily can go 12-14 hours on a charge and consider myself an exceptionally heavy user as I rely on my phone for pretty much everything. I think the camera on the G2 is better as well, although that is coming from a father of 5 who is always trying to get a quick pic of my kids so my priorities are probably different than most.