My colleague Deb Bancroft asked me about this one a month or so ago. I’ve debated writing this long enough. I’m among friends, right?
“Amongst” is the older form of the word. There’s no difference in meaning between the forms, none whatsoever. “Among” is the same thing as “amongst.” My personal preference is for “among,” and as I often say: “Unless I’m reading Austen, I don’t want to see amongst in a book.” And for the most part that’s true.
However, if you’re writing a period piece and the older form makes better stylistic sense, by all means use it. If you’re writing a fantasy piece and you’ve chosen to use more archaic or even obsolete language as flavor for your characters’ speech, by all means use it.
Just don’t use it in your term paper about mitochondrial DNA, okay? Cool.