I own neither but have read tons of reviews of both on line. It seems that the difference between the two amounts to:
1. Aesthetics, i.e. one prefers the look of one over the other (I happen to like the looks of the Wolverine better, but that's just me)
2. Rubber versus leather sole. Some care, some do not. Some who care get the leather Wolverine anyway with the intention of modifying or replacing the sole with a Vibram product sooner or later.
3. Horween Chromexcel, which is generally considered to be a better leather than what Chippewa uses. That said, I've yet to read anything bad about the Chippewa leather, it's just a question of "good" versus "better."
4. Cost. The Chippewa variants are all at least $110-120 less than a full-priced Wolverine. The LL Bean Katahdin is, what, $130 less than the Wolverine?
One thing that does not appear to be an issue is quality. Both are well made. One is not sacrificing quality and buying junk by opting for the cheaper Katahdin.
If price is at all a factor, the Chippewas appear to be unbeatable. If not, it's clear that both are terrific options and it's a matter of taste and requirements (i.e. rubber). I'm pretty sure Wolverine would get a lot more business if they offered the 1000 Mile with a commando sole. I happen to think the Wolverine is "prettier," which might translate into "less rugged." That's debatable, except for the sole. Also, it it were my intention to thrash my boots, I'd for sure go for the cheaper option.