So, some sort of distinction between a high register or elite (“classical”) music tradition and a low register or “folk” tradition is found in a number of different cultures. What's the basis for the distinction?
Speaking broadly because we're talking about so many different traditions here, I would say that classical music is less easily accessible, less intuitive for new listeners, and is usually based on building up variations on a theme according to some established system or pattern. It may seem quite dull to the uninitiated, but it offers great depth and sublimity to those who put in the time and effort to understand it. It's an acquired taste.
Folk music is more accessible, more intuitive, and is usually enjoyable by any unprejudiced listener on the very first try. It's more fun, but you could say that it doesn't have as many layers to it.
Some classical fans really believe that classical is inherently superior music because it's “more sophisticated.” This is easily debunked. When classical violinists try to play a fiddle tune, they often sound stiff and mannered rather than expressive and carefree. Fiddle isn't a lower form of violin, it's just different. Classical is seen as a superior form of music for reasons of class prejudice, pure and simple.
Some folkies really believe that folk music is “more pure” than classical music, which they see as artificial. They're also wrong. Classical traditions and folk traditions have fed into each other and influenced each other for many centuries, in a mutually beneficial exchange. Think of it like this.
If you love a good burger, should you never eat filet mignon? Or vice versa? There's room for both!