I find your question slightly ambiguous, although I see that you want to know what influence superior knowledge of a particular openings has between two players of roughly equal strength.

By "know the opening well" and "vague ideas", are you referring to knowledge of opening theory, or understanding of the ideas/plans of the opening? (For now I will assume you are referring to the latter).

I would say that superior understanding of an opening is definitely an advantage - although the stronger the players, the less of an advantage this is, as a Grandmaster in an unfamiliar position could still come up with decent plans and moves - say the second-best option instead of the main line. But if a 1600 was unfamiliar with a position in the opening, they could easily choose a completely wrong plan or respond dubiously.

And there is also the advantage that the player more familiar with a position (almost any position, in fact) will obtain a time advantage - how much this influences the playing strength of the players obviously depends on the players themselves.

In a nutshell: It depends on the playing strength of the players and the strengths/weaknesses of each player. 

Hope this answer helps you!