That's interesting, IC.
Funnily enough, for me the difference (as I perceive it in my layperson's way) centres around humour. Typically, the Asperger's person is not very humorous or has a very individual humour that is not understood or shared by people generally and is slow to "get" jokes and humour; I think of people with Asperger's as being over-literal and rather ponderous. As far as I understand it, there is no such deficiency in ADHD. Certainly J has a very quick sense of humour and is not at all flat or contained in his own world of meaning in that sense.
But maybe this is all a very caricatured view of mine?
