I just want to point out that SpaceX has not yet successfully put a human in LEO. The moon seems well beyond their technical capabilites at the moment and Mars seems like a fools dream at this point in time.
Getting anything, including humans, to LEO is the hard part though. Once they have brought crew to the ISS and have demonstrated a spaceship flying to the moon, landing and returning to earth they will have solved most of the challenges of bringing humans to the moon. And they make good progress on both fronts.
I don't know whether the surface of Mars (.378 g) or the Moon (.165 g) will prove any less destructive to human health.