Largest differences between neighboring counties of various characteristics

[Verily]

Try Duval and McMullen in Texas.

100.31. But they're also beaten by Perry and Chilton Counties, AL, I think.

And Glascock and Hancock Counties, Georgia are 132.58. (Yes, they do share a, very short, border.)

[Verily]

I was thinking of Hancock-and-Glascock the other day, but couldn't quite tell whether they actually bordered each other or not.

I looked up twelve different county maps of Georgia; eight had them unambiguously bordering, and four (including our own) were unclear either way. None had them unambiguously not bordering. And Wikipedia says that they border each other. So I'm satisfied.

And it would be interesting to know the history of why Glascock County ended up overwhelmingly white while its surroundings are demographically mixed (or overwhelmingly black in the case of Hancock).