Messianic Judaism (bold added for emphasis) should have a few basic tennets:
1) Belief in Y'shua as HaMoshiach (the messiah).
2) An active lifestyle that pursues the Torah as a holy lifestyle set apart to G-d.
3) Support/Identity of Israel and the Jewish people.
4) Adherence to the basic tennents of Judaism (ie: the L-rd is One)
5) Keeps the Sabbath in either an established or growing way.
6) Maintains the Festivals in either an established or growing way.
7) Seeks to root out paganism in doctrine, practice, and theology.
8) Understanding the Messiah and his teachings through the traditions, Rabbinical writings, and Tenach/Torah.
Christians vary in all of the above ways, excluding #1:
2) Christians view the Torah as the "old law" that has since passed and is no longer applicable.
3) Christians view that the Jewish people have been replaced by "spiritual Israel", or more commonly known as 'the church'.
4) Christianity is a seperate religion from Judaism.
5) Christianity has a new Day of Worship, Sunday, and do not recognize the Sabbath.
6) Christianity does not recognize the festivals (ie: Passover, Tabernacles, etc) but instead have holy days such as Christmas and Easter.
7) While many christians are aware of the pagan background of many doctrines, etc... they do not try to eliminate such things, but rather see that G-d has 'sanctified' the pagan structures into Christian traditions, etc.
8) Christians do not recognize either the spiritual light of the Rabbis or the Authority of the Rabbinical council. Instead, Christianity has the 'church fathers', priesthoods, and pastoral heirarchy instead to guide them.