I know of no controlled studies of the kind you describe. You might ask the American Symphony Orchestra League, the Conductor’s Guild, and music-education resources (many on the Internet). When I went to school, score reading was an integral part of all music education, no matter what the major. Conducting as a major is a relatively recent phenomenon, however, and I have been hearing that the emphasis on gestures may be excessive—coming at the expense other skills-development such as ear training and score reading. If this is true, it would account for some young conductors’ inability to fix problems. They beat time; they look good; but they can’t work with an orchestra to clean up passages where there are problems (of intonation or ensemble, for example). Nor do they present a personal vision of a work to the orchestra and, ultimately, the audience.

Both gestures and knowledge of scores are important. Gestures are immediate: you can’t work without them; but neither do you spend a lifetime studying them. Studying scores is a lifetime pursuit. It’s impossible to give a formula for what the balance should be in a course. It would depend on the time allotted and the number of students and their talents. If I were teaching a course, though, I would not teach particular mannerisms as some teachers do. It will certainly require more time if a teacher insists that all students look the same in every detail.