My sense so far is that the charm and unease of the Doctor lies in the extent to which he's able to pass for human. He can be charming, compassionate, perceptive, and then turn down Rose's offer of dinner with her mother, who has only just been convinced that the Doctor might be decent, with a blunt and confused "tough, I've got better things to do." Christopher Eccleston's version of the Doctor, at least, is every bad boyfriend a girl has ever had--undependable, often inconsiderate, consistently winning--with the excuse that he's genuinely alien, and genuinely unaware he's causing trouble or hurt.
Depp's uniquely good at playing aliens in human skin. Sometimes, his lack of humanity is physical, he's the sweet young man with blades for fingers. Sometimes, he looks normal even though he's actually psychotically high, the kind of person who will abandon all responsibility and allow an associate to keep a young woman in virtual sexual slavery without really being aware what's going on. Sometimes, he's almost entirely human, but radically displaced from the only element where he's remotely functional. Sometimes, he's violent, clever, and deeply uninterested in functioning in polite society, except to the extent that it lets him take pretty girls to the movies.
*As a critic, one needs to follow Wu-Tang Clan's lessons and protect one's neck via a refusal to be commital, particularly when one wanders into the Geek Holy Land.