I have an ATM75 that has a battery and/or phantom option. It almost always sounds better on phantom. The battery option is for on location and running on battery power across the board. Taking the phantom power burden off the field recorder significantly improves the battery life of the field recorder. Or if there's any question on the quality of the phantom power being supplied, the battery option takes that concern out of the picture. And useful if going wireless and other options. A couple of OZs for the batt, versus a couple of lbs for the cable.
As far as which sounds better, you probably could have run a few tests in less time than it took to post here. Assuming you have said mic, and are not just considering a purchase. You could also setup a shootout with the various options to verify if any others concur with your thoughts.