I've had a Note prier to the G2 and now N5.
For me N5 is everything that I want in phone, it would hurt if it would be let's say 5.3" that's my ideal size, but I really don't miss more screen that much. Only on the day's I see my father heavy using his Note 3, or my mother with her G2.
The reason I was not happy with the Note 3, was because I've got tiered of hardware buttons and always weird noise making homescreen button (I have such luck that all of mine past Samsungs had something weird going on with the home button - or it's just me being paranoid
Anyway the battery on Note is decent it gets me trough the day with normal to heavy usage ( without games ) when the Note would run on the same pace for a day and 3-5 hours more.
For me it was at first an easy jump to the G2 because of no hardware buttons, and then form the G2 to N5 because im just a phone junkie and I love pure experience, fast device, and everything open source out of the box. While G2 was near perfect after flashing PA or CM on it.. that was still not it, for me at least. N5 is a beast and since I'm using it there is no "devil" in me looking out for some other phone.
Well maybe the iphone, but I've owned 3gs and 4.. and I got bored the same week lol.
For you I would suggest G2 is the perfect option, it has the same if not better battery then N5 (I'm not joking) and Lg skin is not that bad as Samsungs.. but it's not better either.
G2 + dormiax (or what is the name of kernel) + cm, mahdi, or PA and you will be one happy camper!
At the end of the day, trying won't get it done."