In my opinion, the 15 north through Utah to Idaho is much safer than the 80 through Wyoming. Wyoming can be brutal and surprising. Plus trucks drive fast through that state, so when things go wrong, they go very very wrong.
Our kids went to school there and the weather was predictably unpredictable.
Last year right about this same time we got caught in heavy winds in Wyoming coming west from South Dakota. We stopped and pulled off the 80 when the winds got too bad, but then we got back on the road when we saw the truck traffic return fully. We stopped for fuel somewhere between Rawlins and Evanston and my wife went back into the fiver to use the bathroom and noticed it was really cold in there. It turned out that the heavy wind had blown our bedroom window out. It wasn't just broken, it was GONE. These windows are designed to be driven down the road at highway speeds, but the wind was just too much. We had to finish our trip with plastic and duct tape over the window, which wasn't so fun when the wind turned into snow.
I could be wrong, but I think the troopers and other drivers in Utah keep the speeds safer and don't drive as aggressively as in Wyoming. Maybe they aren't in as much of a hurry to get out of there.