The G2 and the Note 3 have large enough batteries to last all day without charging, the Maxx could probably last a day and a half, maybe 2. But that seems fairly useless 90% of the time, because you go home and throw your phone on the charger, that is a nightly habit for me no matter what phone I have, with other android phones I end up charging at least once around mid afternoon, with the G2 and Note 3 though you make the full day (fairly easily I might add)
Now the extra ~500mAh in the Maxx could be useful in certain situations (travelling is my first thought, and camping) but that really is a niche area and the G2 and Note 3 are almost there with the battery so it's meh.
With regards to the close to android experience comment, I would point to the Nexus 5, $349 off contract, only thing is the 2,300mAh leaves a lot to be desired.
Also, I would argue loading custom ROMs and rooting your phone is actually part of the android experience, not everyone will or wants to do it, but the option is there if you don't like the software, change it up, and there are plenty of good ROMs for the Note 3 and the G2.