There is no fundemental difference between 'among' and 'amongst'. 'amongst' might be considered a little outdated - as are 'amidst' and 'whilst' but none has been discarded by the use of its counterpart. It is often more common to use 'amongst' when coming before a vowel - e.g. 'among our friends' - but probably not 'amongst strangers'
Among other things Amongst other things. In general avoid the latter as it sounds archaic.
First amongst equals First among equals. The first is a known phrase (and the title of a novel by a Conservative Chairman and criminal!) and although it sounds archaic and is in fact meaningless it would be the more common usage. ** My webpage