Briley Parkway is much better, absolutely. No reason to be on I-24 through downtown. I'm there all the time and I avoid the I-24/65 combo like the plague.
Besides the RV, I drive a motor coach (charter bus) professionally. I always choose Briley Pkwy around. Going thru requires at least three junctions and multiple lane changes just to stay on I-24. Briley (TN-155) has always flowed way better. Two or three stoplights at the east end, but way worth it.
We spent a week in Nashville last November and Briley Parkway is definitely the way to go. You only have to go through a couple of traffic lights before you reach I-24 and Briley Parkway is pretty good road. I would suggest that those traveling on I-65 go the same route. Once on I-24, the I-65 exit is just a couple of miles away. Nashville is a nightmare of road construction and this route eliminates that.