The tendency of the general public would be to look at that study and say the first method is better than the second method (assuming the general public would care at all, which they don't). That's incorrect. I would only conclude that method is actually better if several other people found similar results for similar methods in separate studies.

People tend to place far too much importance on one paper or one study. In theoretical research this can be okay sometimes, but in applied research this is almost always the wrong way to go.