I like
Beatrix better - it's a little more snappy, spunky, and all that.
Beatrice sounds a little more oldladyish. And the first time I saw it, I thought it was said with a long I, and I thought it was ugly. Then I learned how to really say it, and it really was a lot nicer, but that first thought stayed with me. Or something like that. It's growing on me though.