Messianics observe traditional Jewish holidays such as Purim, Chanukah, etc. Christians do not.  

Messianics observe the biblical feasts of Vayikra (Leviticus) 23 such as Yom Kippur (Day of Atonement), Rosh HaShanah (Feast of Trumpets), Sukkot (Feast of Booths) and Passover. Christians do not.  

Messianics do not observe Christian holidays that were borrowed from paganism, such as Christmas and Lent or were simply concocted.

Messianics do not use Easter bunnies, Easter eggs, Christmas trees, etc., (which are part of Christian tradition in many parts of the world although they are not part of official Christian theology).

Messianics worship on the biblical Sabbath, i.e., Friday evening till Saturday evening, not Sunday. HaShem says the Sabbath is an eternal covenant between Him and the descendants of Israel.  (Sh'mot/Exodus 31:16).  

Messianics cant the Shema, and traditional Jewish blessings that most Christians have never heard of, e.g., the kiddush and the Aaronic benediction.  

Messianics cant the Torah portion in Hebrew at worship services.  

Messianic preaching is mainly from the Hebrew Bible (Tanakh), although references to the B'rit Chadasha are common.  

Messianic Judaism emphasizes the special relationship between G-d and the Jewish people, whereas Protestantism and Catholicism hardly ever mention it.  

Messianic Judaism emphasizes Jewish traditions that do not conflict with the Bible, whereas Protestantism and Catholicism totally ignore those traditions.  

Messianic Judaism asserts that the Torah (literally, "teaching") is still in effect (as modified by Yeshua). Christianity claims that once Jesus "fulfilled the Law" it no longer applies. 

Messianic Jews bar-mitzvah their sons and bat-mitzvah their daughters. Christians don't.  

A Jewish person who converts to Protestantism is referred to as a Hebrew Christian, not a Messianic Jew. 

Messianic Judaism and Protestantism teach the biblical doctrine that salvation is a free gift from G-d, by faith in Yeshua.

Roman Catholicism teaches that Catholics can earn ("merit") all the grace necessary for salvation, and that Moslems will also be saved, even though Islam denies the deity, death and resurrection of Yeshua.  

Messianics do not need to be proselytized into Christianity. We already know who Messiah is and what he did to provide salvation for his people.  

Messianics use the same scriptures as Protestants, including the common translations, e.g., NIV and New King James Version. Of course, it is much more common to find a Messianic who has studied biblical Hebrew than a Christian.
 

Messianics only baptize believers, not babies, and only baptize by immersion, since the practice described in the B'rit Chadasha is actually derived from a mikvah, a Jewish ritual purification bath.