Not Particularly Contentious: GM Skill/Quality strongly impacts quality of play experience.
Only Contentious In a Fake Way: Choice of game system strongly impacts quality of play experience.
My (Possibly Contentious) Thesis: As quality of GM increases, the impact of choice of game system on quality of play experience diminishes (though it is unlikely to diminish to zero).
The Curious Question This Raises: Is the diminishment in importance relative or absolute? That is, does the choice of system stay the same while GM improves, so it's a smaller percentage of a larger whole, or does the improvement in GM quality also diminish the impact of the system?
My Answer: A little bit of both. Relative diminishment actually happens, but I think some actual diminishment happens too, especially when the GM has internalized the lessons of the game (and thus no longer needs to lean on the mechanics) or when the GM more strongly takes ownership of the rules to suit her own table.
1 - There's a great example of this in Tech Noir, a system which has, I think, Internalized the most important lessons from Gumshoe. In my mind, Gumshoe's biggest lesson is to teach the GM that there should always be information to move the game forward, and it has an entire clue and investigation system to make that happen. Tech Noir skips that and just tells the GM that the players should always get a new piece of information. While that's a system example, I think it clearly illustrates the idea of how internalizing a system can produce similar outcomes without actually using the system.
2 - Now this is contentious, especially to folks who strongly support playing with rules as written. Take it as a given that it's an argument I've had many times, a position a respect, but an idea I disagree with. If you disagree, then your answer to the curious question may be different, which is ok.