Lower voltage = higher amphere usage
Higher voltage = lower amphere usage
If you have a 12VDC, 1A power supply, you will be able to power less devices (boards, radios, etc) than say with an 48V, 1A power supply. Higher voltages also means less impact to a voltage drop (regardless of whether it is poe or not). There will be an voltage drop over any cable, and thicker cables will also mean a smaller drop in voltage.
EDIT: Comes back to the amount of Watts available, as was mentioned by someone else a bit further up. 12 x 1 = 12W available on a 12V, 1A supply. 24 x 1 = 24W available on a 24V, 1A supply.