Stefan can't even control his own blood lust. He didn't teach Caroline how to control her blood lust in season 2, though everyone believes he did. All he really did was teach her how to surpress her craving, which is not the same.
And we all know Damon can control his blood lust very well. The only times we saw him lose control was when he was angry or upset, which doesn't make it okay, but it also doesn't have anything to do with the bloodlust itself. So, Damon is the obvious choice.

Stefan can't control his own bloodlust. So how could he help Elena. Damon deals with his blood urges all the time. So he would be able to help her a lot better than Stefan. Even a Stelena fan could see that.

yes yes yes yes.. did i say yes?.... there is NO other better choice then Damon, seriously!

Damon is the one who taught Stefan.. so yeah, the most experienced and OBVIOUS choice would be Damon. But who knows, Stefan will probably try to teach her anyway. :/