Madison to Billings, I94 and I90, have about the same distance and time. 94 might actually be a bit shorter since it is closer to the great circle. Using US212 might shift the distance measure in favor of 90.
If you are going to Cody and east entrance, then I90 to US16 is the clear choice. But if headed to the north or west entrances, than 94 works just as well as 90. 94 can slow you down around the Twin Cities, but 90 is (or at least was) awfully rough across southern Minnesota. 90 lets you stop in the Black Hills.
I've driven both on various trips to and from Chicago.
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I just checked GM - I94 is 80 miles shorter than 90/212, though only 15 minutes faster.
Be careful when using GM around Yellowstone. There's an L shaped segment of park roads, W Yellowstone to N. Entrance that the mapping program refuses to use. That glitch was noted in an earlier thread.