I don't have enough of a background in music theory to offer a sophisticated critique of any piece of music, but I can appreciate the use of critical analysis to partially understand the phenomenology of aesthetics. Allow me to illustrate:

Daft Punk's mashup of "Around The World" and "Harder, Better, Faster, Stronger" (from their Alive tour) is a supremely epic piece of music, and one of the things that makes it so is the fact that it is two songs — each of which is a good song on its own — that go well together. The same kind of thing makes Gounod's Ave Maria good — it's played on top of Bach's Prelude in C Major. If you know something about music theory, feel free to correct me.

Now when I say that a song is a "supremely epic piece of music", I am half-joking. I'm lampshading the Mind Projection Fallacy. The music makes me excited, and happy, and moves me profoundly; and that happens partly because listening to two melodies in harmony with each other makes me more excited. I don't expect others to like "Around the World/Harder, Better, Faster Stronger"; but I expect that for those that like it, this formal property of the music plays a role in their enjoyment.

And of course, that's not the whole story. There are other things that cause me to enjoy this song: There's something about the introduction of the base/percussion line at 1:13, for example. And it probably helps that I was familiar with both "Around the World" and "Harder, Better, Faster, Stronger" when I first heard this mashup. And conversely, not every mashup or counterpoint piece is good.

ETA: Furthermore, my other comment is an example where any attempt at objective criticism fails me.