The handling will be the same on both sizes as long as the inflation is correct for the load. There is no real advantage in increasing tire size solely to run a lower pressure because it will be proportionally the same if tuned for the weight load. However, if you run the psi shown on the RV manufacturer's tire placard, you may benefit from a weigh-in and adjustment of that psi for the actual load.
The reason is simple. The tire must have enough air in it so that the square inches of rubber in contact with the road x the psi is enough to carry the weight on that tire. If barely enough, the tire is "soft" and it squirms around and the sidewalls roll over in turns. If somewhat greater, the tread stays flat on the road and the sidewalls stand nicely and handling improves. If too much, the tire gets hard and bumpy, plus it is prone to skidding. That's true no matter what the tire size is.
My advice is to keep the OEM tire size and tune your psi to the normal load, plus a little for a safety margin. Get to the scales and weight the coach axle by axle or "4-corner" (tire by tire).
Former owner of 2004 American Tradition and several other RVs
Home is in the Ocala Nat'l Forest near Ocala, FL
Summers in Black Mountain, NC