A lot of Christians disavow the so-called "Old Testament", claiming that once Jesus came on the scene, all other laws, rules and history were null and void.
However, as a Jew, I take some exception to that.
Clearly, both Testaments serve spiritual purposes.
As for the differences, the Tanach (which includes the Five Books of Moses, a.k.a. Torah) really is a study in people.
It teaches us what people did - both right and wrong - and how to live ethical lives.
The history is rich, the commandments are fair and the message is the same: EVERY person, regardless of faith, has something to offer in this world and is welcome into the Kingdom of God.
The Gospels are just as important to Christians, as it explains various interpretations of what Jesus taught, through the writings of people who either experienced his teachings or who retold those stories, years after Jesus died.
The caveat, if you will, is that you MUST believe in Jesus before you can go to heaven.
Both Testaments are worth reading, for Jews, Christians and non-believers.
However, it saddens me that many Christians choose to accept only the New Testament and forsake the very foundation from which Jesus was raised as (he was, after all, Jewish, lived a Jewish life and died as a Jew).
Yet, some of those same Christians will pick-and-choose only those parts of Torah that suit their purposes.
Unfortunately, they miss out on so much wonderful insight and history.