Although I don't play classical guitars, I would imagine that the different wood, set-ups, make them more playable from each other and sound different. But a good guitarist doesn't really need a great guitar to sound good, if you know what I mean.
Being a friend of Gary Paul, les Paul's grandson, I have played a bunch of electric guitars and while I can play each one of them well, I do prefer the sound and playability of a 1959 Les Paul over the newer ones that I own. LOL
Happy Listening.