I am no musicologist but I am a classically trained musician. One of the key observations I have been made awaree of in the last 3 or 4 years since I discovered traditional music for myself, is that it is "All in the rhythm". Listen to a "classical violinist" and a "fiddler" play an up-tempo tune and each will give the same tune different qualities. The instinct of the classical violinist is to seek out the "phrase" in the tune, in other words, its lyrical quality. A Violinist tries to make their instrument "sing". That is usually what will dominate their interpretation.
The fiddler on the other hand, will usually seek out the rhythm of the tune and that will be the characteristic that is emphasized or "comes across" most strongly in their interpretation. Which is correct?
The numerous settings of traditional tunes in classical music have produced some wonderful pieces in the classical repertoire, but they do sound "different" to their traditional origins. Try dancing to some of them!! That is the key, it's the dance origins of traditional playing, where the emphasis is on the rhythm, which gives this music its character. They were written to be played with a rhythmic emphasis and I believe it isn't until classically trained musicians "discover" this and put less emphasis on phrasing that they start to get the "feel" of traditional music. The best players manage to combine both elements. I know the above is a sweeping generalisation but I have observed it to be true on several occasions.