I don't believe sociopaths or psychopaths are at all appealing. (And the terms are synonyms, no matter what some of the applingly stupid dialogue would tell you.) I don't really believe this Sherlock gives a shit. It's remarkable how much that lessens the viewing experience.
I see Cumberbatch's Sherlock as an extreme version of Doyle's character, one that has his empathy toned down and his narcissism ramped up. I don't see him as a sociopath, but neither do I see him as someone on the Asperger's spectrum, either. In terms of his relationship with others, I'd largely agree that he doesn't "give a shit." The puzzle is more interesting to him.
This is how I describe the difference between Cumberbatch's and Miller's characters. Cumberbatch is a Sherlock Holmes who hasn't looked into the abyss yet, he will eventually, and he'll get burned because of it. Miller has looked into the abyss, got burned, and he's a better integrated personality because of it.