I can confirm, at least, that the Holmes we have the honor of talking with is the original one, written by Doyle himself. As I stated elsewhere, I have read all of Doyle's Holmes series, and even have them one room over from me as I type this. That is unmistakably Holmes.
Man, I know the stability of reality is udner threat and everything but... still, THE Sherlock Holmes.Awesome.
So it would make sense if it were the same Moriarty, then, although perhaps it's not... From what I've seen he seems QUITE aware of modern technicalities, moreso than Holmes anyway.
Maybe multiple-media franchises like Holmes, who's had everything from books and movies to videogames, will be amongst the first to seep through, alongside the oddler, more fundamental or archtypical stuff (Cinerella and the plague man came through because they're ancient concepts and thus have more weight behing them, and Holmes has strength due to it's multimedia nature?
Course if that were true we could end up with more than ONE Holmes running around.