For HiME, I'd say my favourites are ep. 3(?) where Mai meets Kagutsuchi the first time. Ep. 8, because the ending of that ep was sooo increadibly evil. (Akane/Kazu-thing). After that, it's basicly 17-25. Heavy drama.
As for Otome, my favourites so far are the first episode and ep. 7, which simply is the best one yet. So many good things happened in ep. 7 it'd probably take the whole day to write down all of it.
(Meister-robe! Mikoto! NagixMashiro! Arika in that workers outfit! MATERIALISE-song! Plot! Fights! Contracts! etc.)