And trying to 1v1 another cavalry lancer is a good way to diminish the amount of kills you can get that round. Even assuming you are very confident your timing and maneuver is better than the other guy, that cavalry lancer is a much greater threat to you, than an infantry guy who is engaged and actively fighting (hint, they're distracted).
Any melee cavalry is best used going after enemy infantry (using risk assessment to go after the least likely threat to you and your horse), also try to take out the largest threat to you or your team if you have the opportunity (go after a pikemen, or a heavily armored infantry who is tearing up your infantry). If your team is dying then I up my risk factor and take more risks. Also, if the enemy cavalry is destroying our team then I will usually up the risk factor I'm willing to take, and will go head-on versus enemy cavalry. But typically it seems like my team does better when I'm attacking and killing enemy infantry, than trying to play defense (or try to be a buffer) against enemy cavalry versus our infantry.
One of my biggest pet peeves is seeing our cavalry race off at the beginning of the round and try to engage the enemy cavalry. It's one of the worst uses of your cavalry as you can make. Second biggest pet peeve is seeing your cavalry circle around a group of enemy cavalry or infantry, and basically allow themselves to be kited for a majority of the round.