Similarities are
- Christianity is a Pagan-Jewish synchretic religion, so obviously has a lot of similarities
- both worship YHWH
- both are monotheistic
- both use the Jewish scriptures (though naturally Christians only in part)
Difference are
- Christianity believes messiah has come, Jews do not
- Jews believe in a fully human messiah, Christians think messiah is God/son of God
- In Judaism there is not supposed to be a 2nd coming-- the messiah is supposed to put an end to things like war and death; in Christianity, Jesus is supposed to come again to complete the prophecies
- Jews don't believe God can be born in the flesh, Christians believe God was born in the flesh
- Judaism teaches the Torah will never be changed or added to; Christians changed & added to
- In Judaism the tanaka is the only scripture; in Christianity, there is the New Testament
- Judaism teaches their covenant with God is forever (even when the messiah comes); Christians teach the old covenant is brokenand there is a new covenant
- Judaism sees God as 1, not three; most Christians are trinitarians (father, son, holy ghost)
- Jews don't believe in fallen angels-- Satan is under God's control; Christians think Satan is a fallen angel who rebels against God
- to Jews, there is no eternal place of torture after death; Christians believe hell is an eternal place of torture
- To Jews, there is no such concept as 'salvation'; Christians believe in Jesus being the savior
That's pretty much the tip of the iceburg but gives a basic overview