I honestly don't care for either but my pick would be
Beatrice. I prefer the look and sound of it slightly more. Plus, it sounds more of an "actual" name to me and not something too fictional as what '
Beatrix' conjures up.
I have tried to warm up to
Beatrice but I just can't. The name is too dated for my taste and just conjures up images of a harridan-type. Like, the given name of an old and mutual disliked teacher that everyone wishes would retire already.