Yeah, that's what I was saying, they're the same.
Just imagine a novel, or a movie. The hero has a problem, and needs to overcome obstacles to solve that problem. That's the story.
Obviously, that's also the puzzles when it goes from book/movie to adventure game.
I just can't see how they could be separate so I can't say which is more important, they're the same thing as far as I'm concerned. What makes a good adventure game IS making sure that they're the same thing (so, no puzzles that have nothing to do with anything, for instance).