Do Christians receive the same inheritance as Messianic Jews?

God does in fact have a special relationship with the Jewish people. That special relationship stems from the fact that Israel is God's chosen nation (the nation through which God would bring Salvation to the world).

And Looking back at History we find that that relationship began with Abraham:

All Scripture is quoted from the King James translation unless otherwise noted.

Genesis 15:3 through 6 And Abram said, Behold, to me thou hast given no seed: and, lo, one born in my house is mine heir. And, behold, the word of the LORD came unto him, saying, This shall not be thine heir; but he that shall come forth out of thine own bowels shall be thine heir. And he brought him forth abroad, and said, Look now toward heaven, and tell the stars, if thou be able to number them: and he said unto him, So shall thy seed be. And he believed in the LORD; and he counted it to him for righteousness.

But Abraham had a elderst child through Sarah's handmaiden.

Genesis 16:15 And Hagar bare Abram a son: and Abram called his son's name, which Hagar bare, Ishmael.

But God did not choose Abraham's elder son as his chosen Nation.

Gen 17:18 through 22 And Abraham said unto God, O that Ishmael might live before thee! And God said, Sarah thy wife shall bear thee a son indeed; and thou shalt call his name Isaac: and I will establish my covenant with him for an everlasting covenant, and with his seed after him. And as for Ishmael, I have heard thee: Behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation. But my covenant will I establish with Isaac, which Sarah shall bear unto thee at this set time in the next year. And he left off talking with him, and God went up from Abraham.

God again chose not to continue his chosen Nation through the eldest son:

Gen 25:21 through 26 And Isaac intreated the LORD for his wife, because she was barren: and the LORD was intreated of him, and Rebekah his wife conceived. And the children struggled together within her; and she said, If it be so, why am I thus? And she went to enquire of the LORD. And the LORD said unto her, Two nations are in thy womb, and two manner of people shall be separated from thy bowels; and the one people shall be stronger than the other people; and the elder shall serve the younger. And when her days to be delivered were fulfilled, behold, there were twins in her womb. And the first came out red, all over like an hairy garment; and they called his name Esau. And after that came his brother out, and his hand took hold on Esau's heel; and his name was called Jacob: and Isaac was threescore years old when she bare them.

In each of these cases what we find is that God deliberately chose the ones who would best serve him. This remained true throughout the history of the Jewish nation. Some examples are Jacob (Israel), Joseph, and David.

God has never abandoned the Nation of Israel, however he has put conditions on their prosperity:

2nd Chronicles 7:14 If my people, which are called by my name, shall humble themselves, and pray, and seek my face, and turn from their wicked ways; then will I hear from heaven, and will forgive their sin, and will heal their land.

That promise is still in effect today, but it no longer pertains only to Israel:

Matthew 23:37 and 38 O Jerusalem, Jerusalem, thou that killest the prophets, and stonest them which are sent unto thee, how often would I have gathered thy children together, even as a hen gathereth her chickens under her wings, and ye would not! Behold, your house is left unto you desolate.

We learn from this Scripture that because of the repeated ignoring of the prophets, the promise of Salvation no longer is exclusive to the Jewish Nation:

John 10:14 through 16 I am the good shepherd, and know my sheep, and am known of mine. As the Father knoweth me, even so know I the Father: and I lay down my life for the sheep. And other sheep I have, which are not of this fold: them also I must bring, and they shall hear my voice; and there shall be one fold, and one shepherd.

From this we learn that Jesus intended to include other Nations in Salvation, and that would consist of those whom he knew and they knew him. This may be thought of as the basis for Salvation and is why we are to confess Jesus as our Lord and savior.

If Jesus meant that there should be separate rewards for Jew and Gentile why would he have said:

Mark 16:15 And he said unto them, Go ye into all the world, and preach the gospel to every creature.

Most Christians will likely agree on the basic principle that the Children of Israel, down to the present day have a special relationship with God, but that at this stage, we don't know what that relationship is, exactly. Jesus' parable of the workers in the vineyard (cf. Matthew 20:1 ff.) might apply here, with the Children of Israel representing those hired earlier in the day, and Gentile Christians representing those hired at the eleventh hour. On the other hand Paul taught the Galatians (3:28-29) that there is "neither Jew nor Greek, slave nor free, male nor female, for you are all one in Christ Jesus. And if you're Christ's, then you are Abraham's offspring according to the Promise." [RSV]

Besides, Jesus was a Jew. Christians believe nearly universally that we are part of the Body of Christ, which makes us Jews, too.

By the way, it should be noted that depending upon their exact beliefs, most Messianic Jews would be considered Christians.