If Jesus was a rabbi, then he was not that different from Hillel, except on divorce, so that does not explain his significance. His followers did not form a School of Jesus comparable to the School of Hillel or the School of Shammai.
Where does Jesus fit into the rabbinical schools of his time? In the dialogues that have a rabbinical structure, he overwhelmingly comes out with a position similar to the House of Hillel. However, Hillel did not expect a messiah (Babylonian Talmud: Tractate Sanhedrin, Folio 99a). With its radical ideas of national purity, it would seem that the House of Shammai would be much more interested in a messiah who would drive the impure from the land and establish a kingdom where everyone would follow the Law.