I don't have any comment on Dr. Who since I've never gotten into it although the feeling I got is the Doctor is a pretty cold character in a lot of respects don't know anything about the Master since I don't watch.

But yes, there isn't an underlying gentleness to either character in Potter which is I suppose is one part of the reason I ship them, neither is easily designated by writers as "the girl" of the pair.

*sigh* I'm still waiting for my next fandom. Hopefully soon.