My father has the Moto G and I do have the LG G2.
I don't see exactly why you compare the two devices, as the LG G2 is without doubt superior in terms of hardware.
But - regarding the battery, the Moto G is generally the big winner here (unless you are going to root your G2).
My father's Moto G lasted for 3 days, 10 hours with 2h 32 minutes of screen ontime and STILL had 47% left.
The G2 might be able to do the same, but I'm generally a heavy user.
Hope this helps!