A blowing vs sucking competition?
This is also true in Washington (state), where the Cascades are more than a geographic boundary line: except for a couple of counties on the wet side, the mindset changes dramatically when one crosses the mountains. See here for a visual aid, if you like.
There is a constant low-level undercurrent of grumbling on the dry side as to how they should split off and either join Idaho or form an entirely new state (“Liberty” seems to be a perennial favorite). The main idea is that they won’t have to subsidize the damfooltaxandspend liberals and their harebrained schemes any more; the fact that the money flows in the opposite direction has no bearing in what they know to be true.
And it can be not so good-natured at times. I’ve been harrassed in Columbus due to my Michigan sticker, and I have been told there are certain parts of town I shouldn’t even park unless I want to get keyed.
This isn’t really an inter-state rivalry so much as an international one, but Michigan loves making fun of Canada. I don’t know if they still accept Canadian coins in Michigan but when I was a kid they were interchangeable with U.S. quarters. So we basically make fun of them because we are almost Canadian ourselves. There’s also a friendly rivalry between Yoopers and Trolls in Michigan (Upper vs. lower peninsula.) But since there are only about four people who live in the UP, it doesn’t come up much. 
I live in New Jersey, and I like New Jersey. I don’t live in New York, and I like New York. Thing is, nobody in New York can possibly conceive of why anyone would want to live anywhere else, hence the pissing all over New Jersey. And boy did I piss off a Long Island native when I told her it was a lot like the Midwest!
Thank you for adding Fishtab to my commuting vocabulary! I knew it was lacking something. I’ve just been calling them “effing boat people” all these years.
For the Illinois vs Wisconsin battle I give you a nice little song compliments of Chicago DJ Jonathon Brandmeier