The Jewish and the Christian religions share the same scripture in what the Christians call the Old Testament and the Jews call the Tanakh.
It's important to point out that the Christian faith is originally a Jewish faith. The book of Acts, which many historians regard as a well-written work of history in addition to being a religious book shows that the initial believers in Yeshua (Jesus)were all Jews. What's more, they were reluctant to bring gentiles into the faith until specifically instructed to do so.
The misunderstanding about the nature of the Messiah between Christians and Jews results from a failure to read the Old Testament comprehensively.
Long before Yeshua ever came, Jewish scribes and rabbis had a quandary. There seem to be two sets of Messianic prophecies in the Old Testament. The majority of prophecies portray the Messiah as a righteous judge and conqueror. But a specific set of prophecies portray the Messiah as a suffering servant. The most obvious of these prophecies are related in the book of Isaiah, and specifically in Isaiah 53 which says:
“Who has believed what he has heard from us? And to whom has the arm of the Lord been revealed? For he grew up before him like a young plant, and like a root out of dry ground; he had no form or majesty that we should look at him, and no beauty that we should desire him. He was despised and rejected by men; a man of sorrows, and acquainted with grief; and as one from whom men hide their faces he was despised, and we esteemed him not. Surely he has borne our griefs and carried our sorrows; yet we esteemed him stricken, smitten by God, and afflicted. But he was pierced for our transgressions; he was crushed for our iniquities; upon him was the chastisement that brought us peace, and with his wounds we are healed.”
Not only does this passage paint a clear prophetic picture of the suffering and death of Christ for sin, but it also prophecies that he would be rejected by his own people. When teaching on this passage, Jewish Rabbis tend to read the suffering servant as Israel, not Christ.
It was and is difficult for Jews to reconcile the suffering image seen in Yeshua with the conquering Messiah seen in so many other prophecies. What they miss is that all the Messianic figures of the Tanakh - such as Joseph who saved both Egypt and his family from starvation, and King David - suffered and were rejected by their own people before they became rulers. The picture given in Christ is, in fact, consistent with both the prophecies and the Messianic figures of the Tanakh.
More than this, however, the New Testament indicates that the so called "Second Coming" will not occur until there is a massive acceptance of Christ as Messiah among the Jews: "For I tell you, you will not see me again, until you say, ‘Blessed is he who comes in the name of the Lord.’" Matthew 23:39
In the Old Testament prophetic book of Zechariah, when the prophet was speaking of the coming of the Messiah, the prophet states:
“And I will pour out on the house of David and the inhabitants of Jerusalem a spirit of grace and pleas for mercy, so that, when they look on me, on him whom they have pierced, they shall mourn for him, as one mourns for an only child, and weep bitterly over him, as one weeps over a firstborn.”
This passage states some extremely important things. The speaker, presumably God, identifies himself with “him whom they pave pierced,”and talks about himself as the “firstborn” and “only child.” Speaking of the end times, and excessively Messianic, this aligns perfectly with what Christ stated in the Matthew passage.
But what of the seeming difference of the God of the Old Testament versus the God of the new? The picture of God that Christians have in Yeshua was of a God that had specifically come for the purpose of providing a means of salvation, and would come a second time to judge the world. Regardless what else people think of him, even Jews and Atheists will freely admit that Yeshua was a good moral teacher. But Yeshua came specifically to die in order to appease God's wrath against sinners. Throughout the Old and New Testament, God's love and grace are always balanced against His justice and judgment. Nothing is more telling of this than Messiah himself. Consider all the passages in the Old Testament where God DOES pour out wrath and judgment on people. This is always preceded by a call to repentance and a period of grace. Noah is said to have preached to the world prior the flood. Lot preached to Sodom and Gomorrah before it was judged. Or consider the book of Jonah. An unwilling prophet was sent to a gentile nation to preach repentance. And they repented and were spared. And then Jonah has this conversation with God:
“O Lord, is not this what I said when I was yet in my country? That is why I made haste to flee to Tarshish; for I knew that you are a gracious God and merciful, slow to anger and abounding in steadfast love, and relenting from disaster. Therefore now, O Lord, please take my life from me, for it is better for me to die than to live.” And the Lord said, “Do you do well to be angry… And should not I pity Nineveh, that great city, in which there are more than 120,000 persons who do not know their right hand from their left…?"
Contrast that with Christ's dying words on the cross, "Father, forgive them, for they know not what they do!"
God's justice AND his love are shown consistently in both Old and New Testament.