I am aware that some people avoid freeways, though I'm not sure the usual reasons apply here. I've driven the Buffalo-Gillette stretch of freeway (3 times). It's not busy or particularly rough. The only town on 14 is Clearmont, and I wager there's more to see in Sheridan (I've stopped there for dinner) or Buffalo. Taking 14/16 adds 30 miles to a 70 mile drive. That's a relatively big detour with little apparent gain. And the OP doesn't sound like one those RVers who religiously avoids freeways.
The alternatives for crossing the Big Horn Mtns do get a lot of discussion here. 14A is on my bucket list. I've already done 16 and 14.
As for 14/16 being suitable for trailers - I don't see why not. As I said the terrain is basically the same - flat and straight. But any one can take the time to examine the route in great detail with GM sat and streetview.