Brave Little State here, a podcast from Vermont Public Radio where we answer listener questions about Vermont. As luck would have it, our most recent episode addresses this very question:

"What is the beef between Vermont and New Hampshire? And is the feeling mutual?"

Our reporter Lexi Krupp found that this rivalry traces back to squabbling over the actual line that divides Vermont and New Hampshire today -- the Connecticut River. In 1933, Vermont sued New Hampshire over where along the river the border fell. The rub was over which state had the right to tax power plants along the western shore. The case made its way up to the Supreme Court. And to settle the dispute, the judges went back to colonial documents, declaring the boundary at the low tide line on Vermont’s side of the river where it remains today.

Around this same time was also when the separate political identities of Vermont and New Hampshire really started taking shape. For years, the states had been tough to distinguish. They were roughly the same size and the same population of mostly farmers. But then there was a big shift -- New Hampshire really became much more defined by the large-scale industrialization. And in Vermont, agriculture held on a lot longer. Partly because of these differences, Vermont developed this reputation of small, tight-knit communities. Think “back to the landers” in the 1960s and ‘70s, when all the hippies came here. And in New Hampshire… because of the rise and fall of big mills and factories, a more libertarian political identity emerged with an emphasis on letting people do as they please without the government or anyone else getting involved. Think “Live Free or Die” and no income taxes.

You can find our full story here: https://www.vpr.org/podcast/brave-little-state/2021-09-23/vermont-vs-new-hampshire-whats-the-beef

There's also some good back-and-forth about all this in the r/Vermont subreddit: https://www.reddit.com/r/vermont/comments/pwglgr/whats_the_beef_between_vermont_and_new_hampshire/