Here’s an interesting article on how jazz and classical music wire your brain differently.
Researchers at the Max Planck Institute for Human Cognitive and Brain Sciences studied the brains of thirty pianists—half jazz players, half classical. They found, the Institute reports, that “different processes occur in jazz and classical pianists’ brains, even when performing the same piece…”
While jazz improvisation may better teach creativity, classical training, as neuroscientist Ardon Shorr argues in his TEDx talk above, may better train the brain in information processing. These studies show that the effect of music on the brain cannot be studied without regard for the differing neurological demands of different kinds of music, just as the study of language processing cannot be limited to just one language.
As a classically trained musician (okay, an out of practice, amateur one at best but I did put significant time and effort into it in my youth), I can vouch for taking a jazz improv class once and being completely out of my depth. But the other students were all jazz musicians and nobody was really interested in bringing me along as a beginner. I also took a class once called “far out improv” with other classical musicians and a teacher who was specifically interested in teaching classical musicians to improvise, and I remember that being very cool. I’ve never heard or experienced anything like that since so it must have been unusual.