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

Is the week before or the week after French Quarter Fest 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?