The two are entirely separate. Each is entirely valid in its own right. DR of course is how you used to fly IMC before radio aids. No doubt pilotage is how people flew for a long time before they started to worry about calculating wind direction.
For the PPL and CPL we use a combination. DR is "corrected" by pilotage.
It is important to realise they are separate as you have to adopt a navigational style that works effectively for you. We have seen on another thread what happens if the pilot becomes obsessed with map reading. Once he becomes 'lost' he feels his navigation has thus broken down. Of course his navigation is still valid until he either fails to arrive at his waypoint at his computed time (-ish) or some other visual cue now confirms an erroneous position.