For me, it comes down to one of these two. Louis Armstrong's ensembles were the first to feature just one person at a time improvising, which was essentially one of the first time solos were used in popular music in America. The Beatles, however, were one of the first groups to have a consistent line-up, making them one of, if not the first "band", along with their exploration of recording techniques.
For me, it's Louis Armstrong. Without him, you don't have people such as Miles Davis, Coltrane, and hundreds who came after Armstrong who built on his ideas about improvisation and soloing.