Nothing. Judaism is for Jews while Christianity is for Christians. The Israelites today in Israel are the tribes of Judah, Benjamin and Levi (are those people who are assigned/responsible in religious privileges in the Jewish synagogue)thus they're within Judaism. If you convert to Judaism then maybe you could not accept that Jesus was the Messiah who came last 2000 years. Read Matthew 28:11-15. Jews only believed that Messiah will appear once to save them from intruders. In Christianity, we believed Christ was the Messiah (who crucified, died in the cross & resurrected to life) and we wait His 2nd Coming to save all mankind. In his 2nd coming there will be 144,000 people coming the 12 tribes of Israel (12,000 for each tribe), Revelation 7;4-8, also great multitude, Revelation 7:9. Anyway if you want Judaism, it's alright. However, what about the lost ten tribes of Israel? In our times today, they're now believing Jesus was the Christ who will come again and they are not worshipping any forms of idolatry unlike before where God vanished them their identity, tongue, flag and true religion because of idolatry. As Christ said worship the Father in spirit without the aid of idols. God created us to worship Him directly without idols but to many they made idols to worship thay they made, that is exactly opposite what God commanded to us.