I just shelved my Note 3 shortly after popping the SIM into my brand new G3. the UI on the G3 puts TouchWiz entirely to shame, has zero lag, extremely snappy, better battery (my N3 got to 49% just sitting in my pocket all day at work, 12 hour shift--my G3 came home with 79% after the same but with everything turned on, as i've not changed a thing since it's brand new)
there is hardly any bloatware, and while i like the G2 UI in regards to showing off that beautiful screen, i must admit they did well with the flatter UI used on the G3. it has an Android L type of look.
the phone overall is nicer looking, and i no longer have to worry about smudging that chrome surround that is standard fare with Samsung phones, but if there is one thing i will miss, it's the S-Pen. without that, especially with KnockON and KnockCode, i must learn to live with an extremely greasy screen since my dirty fingers now have to touch it vs. the S-Pen, and i lose Pen Window. it does offer Multi-Window though, and the speed of the UI and features such as Smart Notice as well as superior battery is more than enough to make up for an accessory that benefited the Palm Pilot more than a 21st Century device.
I'm not sure why there are all these complaints about battery life. my Note 3 got through the day but needed charging as i got home and i couldn't use features such as WatchON remote as i'd be pretty low on charge by the time i got home. this G3 can easily make it two days before getting that low given the same usage.
Maybe it's that my eyes are uber sensitive to bright light, but the brighter-than-the-sun even at lowest dim setting of AMOLED gave me major eye strain, enough that reading ebooks on the Note 3 was painful, and i later bought a Tab 4 7 to use as an e-reader instead, but AMOLED remains too bright for me even at the lowest setting, it is like, at least to me, akin to staring into a star. this also happened with the PS Vita handheld. then comes the oversaturated colors, sure they make TouchWiz nice to look at, but other than that it's too loud. i prefer the more muted colors of the G3's screen and how it looks dim enough to be comfortable even at a higher brightness. it is more like looking at pages of a book, easy to use and easy on my eyes.
to be fair, the Tab 4 7 also uses more muted colors, and doesn't oversaturate.
AMOLED also has the sad reality of being a major battery hog while in use.
As far as a phone goes, i hardly use it as one. i work a job that is bad about killing smartphones so i pair to my G Watch and it stays in the pocket all day long, with my watch being the main interface during work hours. i keep a Samsung Convoy 3 (think rugby and military rugged spec) as my primary phone for email, messaging, music playback, bluetooth and other use. the G3 is just used as a data-enabled tablet as well as a backup phone #.