First turn, both can fire arrows if they've got it.
Second turn, if one's a COMBAT, both duel in close quarters, and neither can use
horses or archery. If both are archers, it's an archery duel. If both are
knights, they're both in mounted combat.
The only point this brings up is that maybe cavalry who are forced into close
combat (ie. front-line duty) should still get some bonus, but not the full
bonus they normally get from their mobility.
P.S. Can horses get killed in combat?