Since the question is who had the most impact on HISTORY (not just musical history), I would argue for Van Cliburn, because his breakthrough on the international scene (including Russia) was instrumental in breaking down the cultural isolation of the Soviet Union which helped contribute, eventually, to changing relations between the US and the USSR and the Cold War's end.
His musicianship opened and softened Soviet political and social feelings about America with his triumph at the Tchaikovsky competition
Mary Jane Bolin
When Cliburn went to Russia and won the Tchaikovsky Piano Competition, he generated warm relationships between the U.S. and the Soviet Union and opened the door to cultural and artistic exchanges which had not been possible before this. Although relations between these two countries have waxed and waned over the years, Cliburn continues to be a hero in Russia and among those in the U.S. who remember his tremendous accomplishment. In short the Cold War began to thaw in part because of Cliburn.