Is the week before or the week after French Quarter better to be in town for live music?

I want to visit FQF during a 12 day visit next year. Is there a difference in the quality of the programming of the live music venues in these weeks? Im always looking to see as much as I can from the local legends like the living members of The Meters, Little Freddie King, Irma Thomas and a lot of zydeco.

So are things picking up after, towards Jazz Fest or before, or no difference?