One of the reasons I will take minutemen over Janissaries is because of the way the movement works. My armies (immortal-diety) tend to be range-unit heavy. For most of the action I find my melee units are mostly there for an occasional experience mop up, ZOC, and for city capturing. They wind up not doing the heavy lifting because giving my siege units the experience is more valuable. I think many other players may find themselves making similar decisions.
The minuteman's mobility allows it to scout for my range units, and navigate rivers/hills to keep the rush moving, I will take that over an attack and heal bonus I don't find myself needing anyways.