In light of the reports of construction around Baton Rouge and Slidell, some variation of this route would be advisable:
My choice is I20 to Jackson, Ms. Go south on hwy 49 to Hattiesburg then south on I59 to Hwy 98. Take hwy 98 to Lucedale, Ms. Turn south on Hwy 63 to I10. Then I10 the rest of the way.
I have never used the Hwy 63 portion of this route as I have always stayed on US 98 into Mobile. I don't know which might be better -- but . . .
In Mobile I have always taken I-65 south to I-10 and have
never had a slowdown right through the tunnel. There is some congestion a few miles before you get to I-65, but I have never let that bother me.
My real point of this post--unless there has been some development that I'm not aware of, Mobile has never been a problem for me--full freeway speed and normal speed in the tunnel.