I first heard amongst used when I went to live in England. To my ear it sounds quaint and very “British.” I especially like it in the expression “to put the cat amongst the pigeons.”
If there ever was a difference between the two words, it is lost now.
According to the OED, amongst is
[l]ess usual in the primary local sense than among, and, when so used, generally implying dispersion, intermixture, or shifting position.
But as Fowler said many years ago,
Such a distinction may be accepted on authority, but can hardly be made convincing by quotations even on the liberal scale of the OED.
He goes on to speculate that the reason that one or the other form hasn’t fallen out of use may be owing to “the unconscious desire for euphony or ease,” and illustrates his opinion this way:
few perhaps would say amongst strangers with among to hand, amongst us is easier to say than among us.
For American speakers of English, the question is irrelevant. Americans say among.
I hope that British speakers will continue to use amongst whenever they feel like it.
Quotations with Among and Amongst
… the legal entities known as trusts and too little time on the kinds of conversations that will help ensure that trust among siblings is maintained when parents are no longer around to settle disputes.? … (www.nytimes.com)
… storefronts in downtown Robersonville in North Carolina, one of 26 states where deaths now outnumber births among white people. … (www.nytimes.com)
ETHICAL CONUNDRUMS: If all the world’s wealth were divided equally amongst its population, how much would everyone receive? (www.theguardian.com)