I think I'd have to go with the F7, just because I like the bigger phones.
I'd imagine that the battery life would be similar to the S3 if not better since they have same sized screen but the F7 has a bigger battery.
Best screen resolution, I think the better camera, and the most RAM.
However, if you want a physical QWERTY keyboard, then the LG Mach is for you.
The downside of the phone is that the dev community doesn't seem very large for the phone. It seems that you can root it with framaroot, but ROM manager doesn't work if you use that. I can't seem to find any custom ROMs for it either.
So since you said you want a phone with some rootability, disregard everything above...
The next phone I would go for is the HTC One SV.