Units with it heal after attacking too IIRC. However, march units get no special ability to heal other units. Actually, a normal medic will heal other units even if the medic moves, so long as its healing targets do not (only the medic itself wouldn't be eligible for healing then).
This makes march better for units that actually attack, and medic better for units that do not.
March is usually impractical though I'd consider it on warrior GG's and of course when units have easy or free access to it late game (SEALS, mech infantry).