As influential as Blues was, Jazz was even more so. Many who say they are influenced by the Blues actually owe more of a debt to Jazz.
Jazz was also not as limited as the blues and expanded out into many, many different areas. Also, unlike the blues, Jazz has continued to morph and change in significant ways.
If it's this century, it's Jazz.
Beyond music, Jazz came to influence culture heavily, especially in America. In particular, the "Jazz Age". The Jazz age gave america a vocabulary and mind set that, with the exception of a a few cluster of years here and there, I don't think we've ever grown out of.