For me, it would be the G4 hands down.
Screen: The colors on LCD screens just seem more natural to me. I.e. Whites are white, not yellow. AMOLED displays have a yellowish tint to them, which just looks ugly to me. I know that's subjective, but it's a big point to compete between the two. Plus, the active display models of the G4 (and M9, also LCD) everywhere I looked still had sharp, clear displays. Anything I looked at with an AMOLED display was burn-in city. You could barely read them because of how bad it is. This includes at a Verizon store with their demo modes playing. I'll only consider phones with LCD screens over AMOLED.
The G4 also has sd card support and a removable battery. I like options and convenience. Plus I've been burned too many times by phones with integrated batteries. I'll never own one of them again if at all possible. It adds another failure point that could render a phone useless unless you warranty it or pay for repair. I also like being able to add a larger battery if I want.
Those are my biggest points. Both phones are top of the line, both have excellent cameras, and there's plenty good that I'm sure could be said about both. So I look for the differences and try to find reasons not to buy one over the other. There isn't a perfect phone for me, and there were several phones I was looking at. It came down to finding those negatives for my tastes to decide which I would get and I've been very happy with the G4.