For me the answer is quite simple: The interpretations of the characters in the TV series House, Hugh Laurie for House(Holmes, get it? sounds like Homes *rolls eyes*) and Robert Sean Leonard as Wilson. It was essentially Sherlock Holmes but with medical mystery instead of crime mystery (and just as ridiculous at times.
Hugh Laurie nailed the aspects of Sherlock that i find most enjoyable about the character, and by that I mean the most detestable aspects. House is completely arrogant, petulant, childish, pathetic, broken and thoroughly pathetic. He is barely capable of functioning unless working on a case or taking drugs (swap Opium for Vicodin), he is almost incapable of holding an actual relationship with someone outside Wilson and even then it's a deranged one by most standards. The only thing really lacking between House and Holmes is House lacks a brother (which would have been fun to see). We are expected to respect the characters because of their brilliance (and many do, that's been Steven Moffat's whole perspective with Sherlock, the celebration of a brilliant man), but they really do just come of as utterly detestable people, and I enjoy that split.
I don't like Cumberbatch's take on the character but only because I can't stand Cumberbatch. Downey did a pretty good job (the chemistry with him and Jude Law was incredible) though I think he managed that sort of unlikeable yet strangely compelling character acting better when playing Tony Stark. I haven't seen any other on-screen takes of the character (or none that come to mind) so I will just say other than House, the original Arthur Conan Doyle stories up to The Final Problem, anything in the Return of Sherlock Holmes I just don't care about. For me the series ends with The Final Problem.
That's my take anyway.