Going from Bryce to Zion, the direct route, get's pretty marginal going in thru the east entrance. Tight twisty very busy road with lots of vehicles parked on the shoulder and pedestrians wandering across the road. Then you need to get a pass to go thru the tunnel with an RV and there are size limits. On the other hand, it's quite a ways to circle around to the south entrance.
Might not be out yet but check on entrance passes. Bryce, you could just show up this fall but Zion, you needed a ticket for the shuttle bus (and you can't drive into the main canyon)...and tickets were selling out quick.