You have two things to consider, resistance and capacitance. Fat wires have lower resistance so you lose less power heating the cable. Try to keep the wires between controller and stepper short otherwise the capacitance can affect the current sensing in a chopper circuit. Fat wires have more capacitance but not so as you will notice.

A 5 Amp fuse will handle more than 5A but may tire if you flow 5A all the time.

The great AC/DC debate was thrashed out in America by Edison and Tesla.

Edison's problem with DC was it meant a power station on every city block, but as he pointed out, you can't run a motor on AC.

Tesla responded by inventing an AC motor that we still use today.

Edison said the higher AC voltage was dangerous and arranged for criminals to be executed electrically to prove his point.

Tesla won but blew all his money trying to transmit power without wires.

Edison lost but left a corporation behind who told everyone that he was cleverer the Tesla.

Tesla left no corporation so he lost by default even though he was actually much smarter.

OTOH Tesla has a fundamental unit named after him but we measure nothing in Edisons :D