The Dream Lord is a sort of mental projection. He basically doesn't exist, physically. And the Dream Lord is more of a personification of the darknes within the Doctor. His dark emotions were personified as a sadistic, manipulative creep: the Dream Lord.
Also, we can assume that the dark side of the Doctor is a personification of the ugliest things inside him (no offence to the brilliant actor who played him) so naturally he would be slightly less good-looking than the Doctor.) Also they dress alike, given that their shirts and bow ties are the same colours.