Cotton is at least $590 more per 1000 sq.ft. than fiberglass, cellulose, or any other kind of insulation. You'll have to decide if the marginal (read: tiny) performance gains are worth the price.
It would be better to first focus your resources on hanging the ceiling resiliently. If you put 2 layers of 5/8" drywall on drywall furring channels, combined with the SSP clips (sold on this site) and did some good sealing, the type of insulation you used would hardly mattter. Mass, decoupling and sealing are MUCH more important than relying on tiny differences in performance among insulation options to quiet your space.