One problem is that one really needs to be familiar with both species to easily identify them. Beginners are often misled by field guides that suggest that identification is easy, and, consequently, Northern Shrikes are sometimes misidentified as Loggerheads in the winter. Northern Shrikes are bigger than Loggerheads. Northerns have larger, more strongly hooked bills. Some of the less reliable marks mentioned in books include the Northern's narrower black mask that usually does not continue in front of their eye (or continue above the bill), and the Northern's more strongly barred underparts. Both these field marks can be difficult to see in the field. Note, for example, the Northern Shrike in the second photo in this post.
Northern Shrikes are uncommon but widespread winter visitors to Minnesota. Loggerheads are rare and local in the summer. Loggerhead Shrike populations across North America have seriously declined in recent decades. The reasons for this trend are unclear, but probably include widespread spraying of biocides, clearing farm trees and shrubs, and an unfortunate tendency to be hit by automobiles. Predation by house cats, competition with kestrels, and historic persecution by people add to the Loggerhead Shrike's woes (Yosef 1996).