I love both, but
Beatrix has a certain snap to it that
Beatrice lacks.
Beatrice also sounds frillier to me, and I sometimes want to pronounce it like "beet rice" (for which I blame an amusing anecdote I overheard about a French class at my school).
:-)
"How you turned my world, you precious thing.
You starve and near exhaust me.
Everything I've done, I've done for you.
I move the stars for no one."
"Within You"