I just recently went from the G3 to the N6, since Verizon finally got off of their asses. The N6 was the phone I originally wanted, but since Verizon dragged their feet, I got the G3. Once the N6 got released on Verizon, I kept thinking about it, so had to make the change.
For me, the G3 was an exceptional device. The only downside that I experienced was poor screen on time. It never truly impacted me in a negative way, since I am not a heavy user, but something that was very apparent during those times of viewing a video or site for an extended amount of time.
The difference in size is negligible, for me. The N6 just doesn't feel that much bigger; I can one-hand both devices. Obviously the size of the user will change this, one way or the other. I would think those with smaller hands wouldn't want to deal with either.
Screen on battery life, for me, is better on the N6. There is really no comparison as far as I am concerned. The stand-by time appears to be better on the G3. The stand-by time on the G3 was almost magical, especially considering how much it eats the battery with the screen on.
-The N6 feels a touch snappier, but nothing that would have me choose it over the G3.
-I prefer the front-facing speakers of the N6. I used to do the old cup-the-speaker move on the G3 when viewing videos.
-I prefer the camera on the G3, but the N6 offering is no slouch. I take more carefully planned shots, never selfies (I hate that I even had to type that out, LOL), and rarely the quick grab-shoot-go shots, so my experince will be much different than one that shoots everything and lives on Instagram.
-I would have preferred expandable storage and a removable battery on the N6, like the G3 has, but I can live without it. It's really more about control than necessity.
That's my experience with the 2 devices.