The original series of Dr.Who was the worst peice of dog **** I had ever seen... the new series is just as bad! A large budget can make a huge difference e.g. watch an episode of stargate from season 1 and then watch an episode from season 9-10, massive difference in the way it looks.
That's within the same show, though. Increasing the budget of a good show is obviously going to make it seem more impressive, but the show has to be solid enough beforehand for the budget to matter. Giving a bad show a huge budget is akin to shining a piece of shit - it's not going to make the show look more impressive. Hence, the budget is unimportant relative to the show's concept.