While I agree that NOLA will have a better variety of food than Nashville, if you want really good BBQ, then Nashville wins out over NOLA. Overall, there is probably more things in the downtown NOLA area to keep your interest than in Nashville, but given you will only be there for 4 or 5 days (and haven't been to either), both have enough things to keep you busy for your trip. As for music, I think others have hit on the music itself, but if you are more into the history of music and the making of music, Nashville just seems to have a bit more to offer. Both have a lot of history. So I'd ask which might be more interesting to you? In Nashville, there is the Parthenon in Centennial Park. There is Fort Nashborough literally right downtown next the Cumberland river. In NOLA, there is the French Quarter. There are a number of very old cemeteries that you can tour. While Nashville might have the Bell Witch, NOLA has whole host of "ghost" tours to satisfy you with.
Also, Nashville will have some historical homes (The Hermitage, etc.), though NOLA probably has more. Both will have a lot of Civil War sites and museums, though I might guess Nashville may have a few more around the area.
Are you more of a partier? Yes there is night life in Nashville and some very good good locations right downtown especially if your big into Country Music. But lets face it, few places are going to match a night in NOLA.