Irene,
Even if you like pipe organs, there are very few organ music recordings that I know of which have much information so low in frequency. Your statement "I am a music listener" implies that we're not discussing movies/HT here. If that's correct, almost all differences in subwoofer performance below 30hz to 35hz are IMO not very meaningful.
Separate subs allow optimal placement and (assuming that you get that right) they will virtually always provide smoother bass response within their operating range than will integrated subs. OTOH, you may have to do more work to achieve this and -more importantly- maintain a seamless blend with your main speakers.
Good Luck,
Marty