First off you did nothing wrong at all! Its a good thing people are after you, it happens and companies know what happens and knows the best offer wins. Nothing new here. Always pursue the best offers around, its a game these companies play, Google vs. Facebook for example.
The hiring game as nothing to do with you, its a game played between companies. Just be sure to call the person tomorrow and tell them you have a better offer. No need to feel bad, feel good people are after you. Its not the first time this happens. If they really want you they may match your other offer. Good Luck and feel good.