Which Dakota?

There's a good reason to NOT go through ND. For starters, you're leaving from the southernmost part of MN, to the southernmost part of Montana. Going thru ND will add about 200 miles to a 1,000 mile trip. But the biggest reason is the oil boom in western ND around Williston. Lots of tanker trucks on Rt. 2 and I-94, and you'd be lucky to find a barn to overnight in and you'd pay a pretty penny for it. Oil field workers have taken over everything. From your location, I-90 is a straight shot to Livingston, MT.
North Dakota will settle down, but not for a few years. I recently read that they've found massive oil shale deposits in the Willison area in addition to the oil already found, which requires more equipment for extraction, and more years.

There was a recent thread about going from Rochester to Duluth, and how to bypass St Paul. Using the beltways doesn't add much time or distance, though.

I'm not sure why GM ascribes less time to the I94 route, even though the distance is longer.

I've driven both, and consider it a toss up, especially if coming from Wisconsin before the 2 freeways split up. I90 across southern Minnesota is supposed be bouncy (tilted slabs), but I94 has the Twin Cities. I94 has Teddy Roosevelt NP, but I90 has the Black Hills. I90 also skirts the Big Horn Mtns.

When I first drove west on I90 (with a small boat in tow) I crossed those mtns (on US14), into Yellowstone, spending the whole of 6 hrs seeing the sights, and continued on to Livingston and I90 west bound. But the return leg of that trip I took I94, and passed through the Twin Cities in the early morning hours.

I'm a native South Dakotan, but I like the drive through North Dakota better, more things to see, especially in the western part around Teddy Roosevelt NP. Take the freeway or go on US 2 and make sure you stop at Fort Union where the Yellostone River meets the Missouri. Will make your visit to Livingston more meaningful since that's on the Yellowstone also. Good CG's in the NP and no doubt private or county/municipal CG's along the way. Another must see place is at the Mandan village where Lewis & Clark spent the winter of 1804-05 with the Mandan Indians, probably good camping spots nearby but I'm not sure.