Some classically trained can't play folk music or improvise. Some can. Some folk musicians and improvisers can read music. Some can't. Some music readers can barely play, some play beautifully. Some non-readers can barely play, some play beautifully.

Trying to say that one way is better or more musical than the other is silliness. The real answer is that some musicians are pretty good and some are pretty bad. Whether or not they can read has nothing to do with it.

As a side note, the ability to memorize music may be a more useful skill for folk musicians.