I'm in the process of switching from the Note 3 to the G4. So far, I love it! The Note 3 has been fantastic and I loved it but the G4 has basically everything I loved about the Note 3 in a size that's easier to manage. The smaller screen bezels really make it easier to hold as does the shape of the curved back. I can't say that I notice the 0.2" difference in screen size but I definitely notice how much smaller the G4 is overall. I was looking closely at the difference the past couple of days and it's significant. I'm not one that has complained about the size of the Note 3 because even with small hands, I quickly adapted to it. But I can't deny the smaller size & ergonomic shape of the G4 is lovely. I'm also a convert to the slightly curved screen.
Can't give the most accurate answers about battery life as I haven't pushed the G4 long enough yet to get a feel for knowing its battery limitations or benefits (having said that, the Note 3 will sometimes tank out on battery with no real explanation - like today for instance, I went from battery at nearly 70% to under 10% in just over an hour with no video, audio, streaming or any other reason that the battery info could give...and the battery is holding a good change - go figure). However, the G4 supports Qualcomm Quick Charge 2.0 and it does charge up fast! Just pick up a QQC2 adapter from Amazon and watch slickdeals.net to find one for under $10. Well worth it.
I have to say that the camera stunning. In just normal auto mode the F1.8 is really, really a huge difference to any smartphone camera I've ever used. I find the Note 3 struggles a bit with close shots, indoor lighting etc and flash doesn't always work. Tonight I was taking crazy photos of close up, small text in low indoor light and the flash didn't need to fire. I mentioned it to my husband and he commented on how he noticed I was taking photos and couldn't believe that the flash wasn't in use. I honestly had no idea it would make that much difference. I've been happy with the Note 3 camera until I used the G4.
As for the rear buttons, I had read a lot about them and the premise made sense to me. I was prepared for the adjustment curve that many had described of anywhere from a couple of hours to a day. At the end of my first day, I was still having to think about the button placement and I was a little concerned if I'd adjust. Just a short time later, I'm constantly touching the back of my Note 3 trying to turn it on and swearing to myself when I hit the side power button on it last night while watching a short video. The back buttons are just so natural and ambidextrous. I'm definitely loving them.
Couple of things to know, if you can't (or don't want to) get used to the different navigation button layout, LG allows you to customize the layout and even lets you add additional ones. In addition, it's not talked about much but you can long press the running apps button to get to the menu in several apps like the Samsung menu button functionality. Some people love the notification bar button so you don't have to reach to the top of the screen to show current notifications. After having my husband's just-out-of-warranty SGS3 have the capacitive button die (for literally no reason) my preference is strongly for contextual onscreen buttons.
The G4 launcher is far preferable to any other OEM skin that I've used. I always hated TouchWiz but of course any of that can be changed with a custom launcher app. This is the only phone in 5 years that I didn't immediately switch launchers & I'm still using LG's.
I have to disagree with the LG keyboard. It's also preferred to other OEM efforts that I've tried. To me, it's the closest I've tried to SwiftKey. I used it for awhile without complaint but eventually installed SwiftKey since I have a huge custom vocabulary built there...though it had a few features I wish SwiftKey would integrate.
The sound is better out of both the external speaker (with more power) and headphones on the G4. I pretty much expected it from the specs but it's nice that it actually translated into better sound. Obviously, it's still a smartphone and an external speaker will trump what's built-in.
Lastly...performance. I've noticed that my Note 3 would fairly frequently get bogged down and slow to a crawl for anywhere from a second or two to frustratingly long. So far, haven't experienced that with the G4. Time will tell but it definitely feels really responsive. The other thing is that although we have great 4G coverage in our area, my Note 3 has been spending a lot of time switched over to 3G. The G4 has maintained consistent LTE connections.
Honestly, with the design changes that Samsung made taking away my choice of using a micro SD card and swappable batteries, plus the pricing difference... I couldn't justify staying with Samsung. With the current $100 rebate that Verizon has, the 32gb/3gb G4 comes in $50 less than a 16gb/2gb Samsung Galaxy S5...let alone the S6/Edge/+/Note4/5. I was really excited about the camera specs and how close the screen is to what I had and I've been even happier with it than I expected from the numbers.
Lastly, I just want to state that I've loved my Note 3. It's been a fantastic device and run like a champ. So the things I prefer on the G4, I've genuinely liked on my Note...it's just that the G4 has made them an even better experience.
Didn't expect this post to grow so long. Hope it's helpful.