Well.... I have both (the Nexus 6 is mine, the G4 is my wife's).
I have big hands, so the size of the Nexus 6 doesn't really cause me any issues. I will say that the G4 is a bit easier to hold, but that's stating the obvious.
Between the two... I'll say that in terms of raw speed, well, you are kind of splitting hairs. Both phones have blazing fast processors so any difference bwtween the two will be fractional. I will say that the Nexus 6 feels more fluid throughout pretty much everything... scrolling, transitions and animations, etc. Of course, I expected that. The graphics processor in the Nexus 6 is actually more powerful than the one in the newer G4... so between that and the stock vs LG UIs. But looking past the occasional jank, the two are pretty much just fast.
What the G4 has over the Nexus 6:
I prefer LG's back-button ergonomics. I owned a G3 previously and I really got used it. Side power and volume buttons kind of get on my nerves a bit now, even almost a year since I've owned the G3 personally (my wife also had a G3 up until a week ago). Between this and the smaller size, the G4 is a little bit easier to use one handed. If my hands were smaller, this would become more noticeable.
The G4's camera rocks. The thing takes great pictures in most every condition and it rock-solid reliable and fast. And the camera app running it is, by a wide margin, my favorite camera app to use.... it was that way in the G3 and LG took and and added full manual controls to it in the G4. Easy to take a pic, easy to take a video, it doesn't overload the user with options nor does it bury things in menus in different places. The camera in the Nexus 6 certainly gets the job done, but that's the one thing on the G4 that I really wish it had.
What the Nexus 6 has over the G4
Screen: yeah, I know you'll have people talk about color calibrations and gamuts and accuracy. But between the two, I just prefer the Nexus's monster 6" window. MOAR SIZE! That's the heart of it. Everything is better on the big screen... browsing the web, writing an email, watching a video. If you hold it and the G4 side by side, you can see the G4's colors run a little cooler than the Nexus, but nothing extreme. And I run custom stuff, so I can adjust the profile to anything I choose. And the G4's screen will be brighter but I actually don't use my phone much when I'm outside so that's not anything that will bother me.
Sound: The front-facing stereo speakers in the Nexus are great. They are loud, have good range for what they are and are pointed right at yo face! So between that and the big screen, it is a much better multi-media expirience. The G4's speaker is loud, but facing the absolute wrong direction.
UI. I am an unapologetic fan of 'stock' Android. I've used phones from several different OEMs, used most of the major Android flavors;Touchwiz, LG's Optimus most extensively. They just don't compare. Motorola has the right idea; keep Android alone and just sprinkle in some value-added bits here and there. It goes beyond launchers; its windows, dialogue boxes, selection windows, settings... they all just look and feel best on a Nexus. Between that and the more fluid feel, I prefer my Nexus 6
Updates: Nexus phones will always be supported the longest, and get updates the quickest, if that sort of thing is important to you. The original Nexus 7 tablet, released in 2012, received Android 5.1.1 late spring. While the original Nexus 7, Nexus 10 and Nexus 4 most likely will not receive the next version of Android, The Nexus 5 and secong generation Nexus 7, both released in 2013, will get it (and fairly quickly).
Which is the better phone? Depends on what you want and need. For me, its the Nexus 6. For my wife, its the LG G4. For someone else, neither might work. It's subjective.