I prefer Juliet, it seems simpler and more streamlined.
I prefer the more no-nonsense Anglicized spelling, Juliet - it feels a little less storybook to me, and I don't like that emphasis on the last syllable that -ette usually triggers.
I prefer Juliet. Both are pretty, though. I think Juliet/Juliette is very elegant, and charming. I also love Jules as nickname.