Over the past 10 years, Minnesota’s western tier of counties has been creating far fewer manufacturing jobs than its neighbors to the west.
A big driver is the Fargo-Moorhead metro area. Fargo’s Cass County added 1,767 manufacturing jobs over the past decade, while Moorhead’s Clay County added only 46.
Otherwise we're not talking about big numbers here. As commenters have pointed out, most of Minnesota's western border counties are sparsely populated, and the eastern tiers of North and South Dakota are their most populous areas. 
Minnesota counties bordering North Dakota have increased manufacturing employment by 7.4 percent in the past decade, mostly in Polk County across the Red River from Grand Forks. North Dakota’s counties bordering Minnesota have increased manufacturing employment by 12.7 percent over the same period, or by 20 percent if you include Walsh and Traill Counties, for which no 2003 data is available, presumably because manufacturing employment was negligible. (see data below)
Along the South Dakota border, Minnesota counties like Pipestone, Rock and Yellow Medicine saw their already small manufacturing bases shrivel over the past 10 years. Together with Big Stone, Lac qui Parle, Lincoln and Traverse Counties, that little rural strip of Minnesota lost 691 manufacturing jobs over the past 10 years, or 33.9 percent.
Again, not a big number, but it's the opposite of what's happening in the sparsely-populated counties across the border in South Dakota. South Dakota’s border counties added a total of 123 jobs, an 0.8 percent increase over the past decade.
A commenter has pointed out here that South Dakota's eastern border is more populous than Minnesota's western border, so the comparison is unfair. Well, if you remove Sioux Falls' Minnehaha County, and Brookings County from the data, you're left with Deuel, Grant, Moody and Roberts, and their gains in manufacturing jobs have been 30 percent over the past decade.
I’m looking at this data as I work on a story about efforts by neighboring states to poach Minnesota workers and businesses. Comments welcome. Here's a screengrab of the key spreadsheet I'm working with.