I have gone to masses at all of the nearby churches, even on the same day (daughter was sick so I took her to late mass when she was feeling better). Some parishes play Protestant songs, others traditional Catholic, and some play Latin songs. In our parish, the pastor works with the music director to give direction (our pastor forbids Protestant songs and prefers Latin).
So, to answer your question, no, music varies parish to parish. The music director is in charge, and whether the pastor gets involved in decisions is up to the pastor.