Why is the Jewish God of the Old Testament so judgmental and violent and the Christian God of the New Testament so kind and loving?

Certainly there are Old Testament passages that portray a harsh God that many of us would find difficult to accept. For example, God smites the Egyptians and indiscriminately strikes down their firstborn in Exodus, or God comes off like a bad parent who threatens punishment to followers in an attempt to coerce good behavior. Contrary to popular belief, though, some sections of the New Testament reflect similarly disturbing images of God. “Fire and brimstone” Christianity is a legacy of Matthew’s gospel in particular, because it is in that gospel that Jesus tells parables that conclude with various offenders being thrown “into the outer darkness where there will be weeping and gnashing of teeth.” (Mt 25:30).
On the other hand, there are many beautiful passages of a tender, loving, and just God in the Old Testament. These positive images include the Good Shepherd who sustains and protects (Psalm 23), the God who created us individually and calls us “precious” and “honored” (Isa 43:1-7), God as a parent who delights in an infant child, feeds him, and teaches him to walk (Hosea 11:1-4), God who is a “rock,” a “shield,” a “fortress” (the Psalms), and the figure of “Lady Wisdom” who prepares a banquet and invites all to come and eat their fill (Wisdom 9:1-6).
Suffice it to say, it is a misnomer to label the God of the Old Testament (who is the God that Jesus – as a Jew – came to know) negatively and the New Testament God a warm-and-fuzzy-type.