The only person who need even think about phantom power is he who is equipping a studio and purchasing a board and mics, or the performer who wants to use a condenser mic on stage. What phantom power does is reside in the board (or in a separate supply box) and power condenser mics (the high-end, serious recording type condenser mics). It's nice to have a mixing board with phantom power capability. Otherwise, you need an outboard supply box (these come in various sizes from single channel boxes up to eight or more channels), and that means an additional expense and more hassle.

Is phantom power better? It's all electricity, but one could consider it a more stable source than a battery which eventually runs low on juice.

Who else might benefit from phantom power? Bassists and guitarists who are using active D.I. boxes would benefit. Some of these units (such as the Sansamp) can be run on phantom power if connected to a board that provides it. It saves money on batteries, or saves you the hassle of plugging in a power supply, and phantom power won't disappear into the night as battery power can.