The Doctor works best if you want to believe that he is part human but are continually forced to admit that he is not. He is a blue-blooded, two hearted, kind natured Gallifreian.
That's what made Doctor Donna a good story. Honestly, it's in the top5 for all-time-great Dr. Who Stories for me. It wasn't until I sat on it for a while. I mean it was ok but not that special. But what they managed with that arc, the idea of it, is a thing that they've never quite done before (impressive itself in a show with a runtime like that) and it reinforced the basic moral of so many things that they have done. The Doctor needs to be the often benevolent Other, he has to be that, but he's also got his own shit to deal with. While The Doctor should never be malevolent, he should appear at times to be perhaps callous, perhaps irresponsible, perhaps outright disinterested. But he's a clever boy.