I voted My Hime. In my opinion Hime was way better than Otome. Deeper and more fluent plot, better character development and of course great soundtrack - those are advantages of Mai Hime.
For some reason, in the beginning I just couldn't stand the main Otome heroine - Arika. Comparing her to well balanced chara like Mai is just a big joke. But eventually I got just used to her. The only new chara which I liked, was Nina - her personallity and plot where quite interesting, but her hair made me laugh through all the series
I don't think that Otome is bad anime at all. I think it's just created for a bit younger audience, especially first 10 episodes.