What are the key differences between Messianic Judaism and Protestantism?
First thing to keep in mind is there are as many 'flavors' of Messianic Jew as there is any other Jew, we have our own spectrum from 'Reform' to 'Orthodox'. Not surprisingly, this is mostly due to the branch of origin for the M.J., as most tend to keep whatever degree of Torah observance they were raised with. Personally I'm from Traditional Sephardic background, so my level of mitzvot observance is the same as it was, I'm Shomer Shabbat but not quite Orthodox. My wife is from Sephardic Orthodox roots.
I have observed that the less Torah education the Jew who becomes Messianic has, the more Christian theology they tend to profess. Secular Jews, who have little or no Torah education (family not affiliated with a Temple, no Hebrew school, etc.) tend to become pretty much Protestant, except they are still in some ways culturally Jews.
My personal brand of Messianic beliefs share very little with Christians, except I use their accounts of Yeshua's teachings. (Sermon on the Mount and a few others) As a Jew, I'm not allowed to have an Intermediary like a Gentile can, so I never invoke Yeshua's name in prayer as Christians do. As a Jew, I know I must serve HaShem alone, so the 'trinity' theology is prohibited for me as well. As a Jew, I know that Yeshua did not fulfill the prophecies of the Davidic Messiah figure, I only ascribe to him the role of the Messiah ben Yosef, as portrayed in the 'Suffering Servant' passages of Isiah 53. As a Jew, I know Yeshua did not change or abrogate the Mitzvot, no he reinforced the Mitzvot but shed light only on our attitude and kevanna in observance.
In summary, the key differences are:
1. The Nature of G-d
Christians worship Yeshua as divine by the trinity theology, while Messianic Jews are just as Monotheistic as any other Jew, the Shema means the same to us as any other Jew.
2. The Nature of Messiah
Christians claim that Yeshua fulfilled all the Messianic prophecies, while Messianic Jews know not all are fulfilled and await the coming of the Davidic Messiah like any other Jew.
(Some MJ may think Yeshua may return to fulfill this role, but personally I doubt that.)
3. The Nature of Torah Mitzvot
Christians change and ignore Torah laws as they see fit, while Messianic Jews know all 613 are still in force, and observe them in whatever form their fellow Jews do.
Or, what may well amount to the same question, what is the difference between a Messianic Jew and a Jewish Christian?
To me, the term 'Jewish Christian' (and I have known some) is someone who turn their backs on their Judaism and the Jewish community and become Christians. They may be culturally 'Jewish' (locks n bagels jews) but their theology is 100% Christian.
Hope this helps, sorry for the wall o text. If you have not yet, check out Green Gaia's excellent overview thread in this DIR, for another perspective.
Shalom