They both get teleported in an arena and are forced to fight each other in h2h combat (Including their weapons).
With a horse he could win (not necessarily, I believe the Persians had horses as well). But if he doesn't have a horse I don't think he can beat Leo. Leo is far better trained, has a reach advantage and his shield is practucally impassible.
The horse could be killed more easily than Khan, as it's a bigger target, and it's easy enough to avoid, but not outrun. If Khan did manage to trample Leonidas then he'd probably kill the Spartan. Other than that it's all down to skill, which i think Leonidas has more of, basically.