I had the S4 and I miss its screen. Both are incredibly sharp and I prefer the 5.2 in. of the G2 over the 5 in. but as for screen quality the S4 wins since it has excellent viewing angles. Both have great colors though, I always use Professional Mode color mode when using an S4. My G2 does not have very good viewing angles, for some weird reason when I tilt it to check 2 of the corners it turns yellowish and when I tilt it to see the other 2 corners it becomes like a cheap TFT screen with dark blue colors where you can't really see anything.
The S4 has a better camera for sure and I miss it, faster to take pictures and nicer quality. However, the G2 takes less blurry shots thanks to the OIS. G2 has better bokeh effect but that's not the most important thing as it only benefits macros and those are not the only shots that I take.
S4 also has better audio quality.
I miss having real keys. I used the HTC Magic for a year, then the S1 for 3 years and a half and then the S4 for half a year. I don't like the navigation bar, it's annoying, takes screen space, even after modding it to be smaller, and it doesn't behave good since sometimes it doesn't go to immersive mode because some developers didn't add that to their apps.
Overall I prefer the G2 as a phone, smoother and better experience, better UI and better LG apps and features, love it!