Driving from Billings MT to Casper WY?
 

Which of these routes is most scenic?

Billings, Sheridan, Buffalo, Casper: 276 miles
Billings, Lovell, Greybull, Shoshoni, Casper: 325 miles
Billings, Cody, Shoshoni, Casper: 323 miles

Is there some other route that is more scenic that any of these?

HTTY

Haven't been past Buffalo on the 1st option, but really like it south Little Bighorn south to Buffalo.
Think the Lovell, Greybull, Shoshoni would be my choice of the other 2.

Shoshoni to Casper is a VERY dull drive. You will see nothing. It's a two lane road and a 65 MPH speed limit, so it would take about an hour and a half to get to Casper.

However, the Wind River Mountains (right after leaving Thermopolis and it takes you to Shoshoni) are beautiful. That part is worth the drive. I also looked on the map and if you go through any road through the Big Horn Mountains, it's a very scenic. The Shell area is really a nice place to see. Before you plan any drive, be sure to check wyoroad.info, as there have been a few mudslides in that area. It should tell you if the roads are open or not.

Billings/Sheridan/Buffalo is all on the Interstate, easier driving than the two lane roads. It's very pretty in the Sheridan/Buffalo area.

That whole central area of Wyoming is pretty boring and desolate to me. Some of it is almost other-worldly even. I think I'd stick to the interstate on this leg of your journey.