Batteryboxes provide mic powering only, and no gain (gain=amplification). They are very simple devices and outside of build-quality differences and the specific voltage they send to the mics, assuming they work, there is little difference between them, either sonically or electrically.
Preamps provide both power and gain. It is the gain stage where you may hear some minor differences between the different preamps which are most are applicable here. A bigger difference is the form factor, inputs, controls, powering.. all the practical stuff, not the sound so much.
Which you need depends on what you record, how you record it, and your other gear. If you tell us more about what you are recording, we can better direct you.