I am in my second year of a four-year program studying the Bible, its underlying history and theological reflection ("think theologically"). Recently, we have discussed the historical, Biblical, philosophical and theological events surrounding the emergence of Christianity, including a discussion around the differences between Judaism and Christianity. The Old Testament contains the various Hebrew texts that are canonical for us Christians. The O.T. is foundational for Christians, so, what was it that needed to change in a way that required a new religion? The Torah already tells us to help the poor, so what's the big deal about Jesus? Seems like we need more than just another prophet, so I will poke at a few notions here.
Did Jesus believe all people are equal? Is justice the same as equality? I don't think so. Paul's analogy in 1 Cor 12 is that we are all different parts of a body, all necessary, but with different abilities (gifts) with which we can fulfill different purposes. For the moment, I am assuming 1 Cor 12 is consistent with Jesus' teachings. In a few weeks I will dig deeper into Paul's epistles and may have more to say.
Mosaic Law (Lev 23:22) states, "When you reap the harvest of your land, you shall not reap to the very edges of your field, or gather the gleanings of your harvest; you shall leave them for the poor and for the alien: I am the Lord your God." But, I claim, followers of the Law would typically distance themselves from the poor and aliens at "the edges". A follower of Torahic purity guidelines would likely consider those poor people to be shameful (see "Introducing the New Testament" by Mark Allan Powell). Jesus, on the other hand, says we must love our neighbors as ourselves (Mark 12:31, etc.); Jesus pushes Lev 23:22 beyond the generosity a subsistence community would normally practice. Jesus was born into the poorest of the poor and knew (as stated by Powell and Hillary Clinton), that survival in first century Galilee "took a village", but the village of Mary and Joseph was an extension of individual self-preservation (not the same as universal salvation). Judaism does not preclude Jesus' teachings, but Jesus' dedication to service and humility radically ignores the notions of honor and shame that were important to first century peasants under Roman rule. Today, we are not shocked at the idea of service and humility, but it was indeed radical at the time of Jesus' crucifixion.
Jews widely believed in resurrection (except for the Sadducees), although the canonical evidence in the Old Testament seems more abstract than in the New Testament. Jesus seems to have broadly developed the theology of resurrection in terms of whether one deserves resurrection or what salvation means to us during our earthly lives. Hebrew philosophers interacted with the Greeks and Persians and Romans and Egyptians and others; see especially the O.T. book of Daniel. However, it's not clear to me that any first century synagogue focused on eternity. One imagines Jesus' frustration with a holiday like Purim, which outwardly celebrates the cancelation of an edict to kill all Jews (Esther), but cannot be disassociated from the slaughter of tens of thousands of gentiles for almost no reason.
Jesus didn't invent any theology; resurrection and aid to the poor were well understood. Previous leaders claimed to be the son of one god or another, but the sacrifice of the divine Jesus (in fulfillment of the non-sacrifice of Isaac) provides the theology of a god who physically understands humans.