I've never heard anyone express a preference. What does your publisher say? Most of them belong to both. (Technically, I think they have to keep books like they are two publishing companies.)

Don't forget SESAC either... actually i prefer. they pay more and they pay faster and they pay on College Radio Play. Also.... BMI makes it really difficult to get out of.

ASCAP is very easy and offers a lot of carrier building help and tools.

I seriously doubt you'll hear anything bad about any of them. All three are good organizations.