Hi,
I bought the L2 G2 at the end of November (came from an S4), and used it for 3 weeks (before selling it). This was my take on the phone:
Pros:
1) Nice Large Screen
2) Fast and Responsive
3) Great UI (quick reply to sms, draw directly on screen etc.)
4) AMAZING battery!
5) Great camera (can even see the OIS work when shaking slightly)
Cons:
1) Touch was not as sensitive as on my S4 (this could have been an issue on my phone only - I can't prove that this affects all G2s). This made it slower and more difficult to type, as I like to "touch type".
2) Phone has no availability of accessories in South Africa (and limited elsewhere). I had to import a screen protector and case from the UK. Also, for the life of me I could not find any slim case for the phone like I have for my S4 (S4 case weighed 6 grams).
3) According to the specs, phone is NOT much bigger than the S4, but in actuality, it FEELS a lot bigger. I even gave it to a friend to look at (who owns an S4), and his first reaction was "wow, this phone is big".
4) With the slimmest case I could find (that protects the phone on sides and top, bottom), the phone weighs 25% MORE than my S4 weighed with the slimmest, protective case that I got for that. And I could easily feel the extra weight.
5) IPS LCD vs AMOLED - For me, it's night and day difference. The blacks on the LCD look grey contrast compared to blacks on the AMOLED screen. I love the contrast on AMOLED. Also, I personally like the over saturated colours on AMOLED. I want my phone to feel "lively"... not sure why people want a cell phone to look "natural" (like they claim LCD makes it look).
6) Buttons on screen - don't understand why google and LG do this. I didn't like the fact that 10-15% of my screen estate was being used to show 3 static buttons. With the "screen buttons", the screen actually becomes about the same size as a regular 5 inch phone.
7) A friend had an issue with his camera on his S4. I went with him to a Samsung centre. They replaced the camera in 6 hours. To me, this is total piece of mind knowing that the turnaround time is so quick with Samsung. And lets not even mention ADH which just adds to that. I'm not saying LG has bad service, but as they don't have dedicated service centres (nor ADH), I doubt it is as good as Samsung's.
So, I'm now back to an S4 and loving it! There are a few things I will miss about the LG (especially the battery life), but to me, personally, I just prefer the S4.