It's up to you. I think in most cases exclusive means that only the person you are granting those rights to can use the music. It doesn't mean you are giving up one hundred percent ownership of the music to them unless, again, that's what you want to do.
Another thing is some artist will sell non exclusive rights then some one will get exclusive rights. The non exclusive rights still pertain but from that point on no more exclusive or non exclusive licenses can be sold.