My girls did both when they were younger but on two different trips. They are entirely different experiences and both are very special. At the age your daughter is, I'm sure that the BBB would be ideal but there is a significant portion about the hair and a lot of time was spent styling. That being said, there is plenty of time spent on picking out the perfect princess outfit and accessories. Makeup was a really big deal. Overall the experience was phenomenal.
The pirates league was great at indoctrinating your child as a pirate with her own pirate name, taking the pirate oath, fun interaction with the stylist, and great makeup/costumes.
Both have their highlights and my kids loved each one. I think they felt more special being dressed as a princess though. When we were watching the afternoon parade at Magic Kingdom, Aladdin actually blew my little Jasmine a kiss and the CMs do go out of their way to address the little ones as "your highness". My little Belle was actually chosen to be a part of the Monster's Inc. Laugh Floor.
I'm sure they will have something in mind for your little one. IMHO I would go with the BBB if she is at all into princesses. They will find a way, You might want to keep in mind though that the wigs they have at Disney are not designed for comfort and are actually quite scratchy on the inside which may irritate your daughter's head.
Either way she will enjoy whatever you choose.