Wait. It depends on if your opponent only had 1 monster. If they only had one monster, it would not be on the field to take control of, because your opponent would have Tributed it as the activation cost of "Enemy Controller", but if your opponent had more than one monster, and he or she activated "Enemy Controller", offering one of his or her monsters as a Tribute, you could chain with your "Enemy Controller", Tributing the monster that he or she targetted to take control of an opponent's monster (not the one they Tributed). Then, assuming your opponent does not activate anything in response to your "Enemy Controller", the chain resolves backward. You take control of the monster you selected as the target of your "Enemy Controller". Your opponent's "Enemy Controller" does not work, because the monster targetted for his or her "Enemy Controller" was Tributed when you activated your "Enemy Controller".
If you both had more than one monster, and you Tributed a monster the opponent was not taking control of, you would both get the monster you are selecting to take control of (but if you want your monster back, you have to do it in another chain, like woltarr said). Yup.