In this week's parsha, the aseres hadibros are repeated. When I was younger, a guest at our Shabbos table offered me a prize (which ended up being a sticker) for every difference I could find between the Yisro version and that of Va'eschanan. I found ten.
In the fourth commandment, the mitzvah of Shabbos, we find a reference to the subjugation in Mitzrayim that was not mentioned in parshas Yisro. We are told (5:14) "And you shall remember that you were a slave in Mitzrayim and HaShem, your God, took you out from there with a Mighty Hand and Outstretched Arm. Therefore, HaShem, your God, has commanded you to make a Shabbos day." Rashi writes that this is simply a reminder that HaShem brought us out of Mitzrayim in order to perform his mitzvos, of which this is one. In other words, there seems to be no direct connection between Shabbos and yetzias Mitzrayim.
It would seem, however, that there is an intrinsic connection between the mitzvah of Shabbos and the exodus from Mitzrayim. There is no reason to assume that the Egyptians gave us a day off on Saturday. Rather, a more conceivable assumption would be that we had a full seven-day work week. With the exodus from the enslavement in Mitzrayim came the freedom and autonomy to set our own weekly schedule. We are thus commanded to set aside Shabbos as a way of reminding us of this great gift. [However, see the midrash (Shemos Rabba 1:28 and 5:18 which imply that there was a reprieve on Shabbos.]
When immigrants first came over to North America, they were forced, so to speak, to work on Shabbos, creating a new flavour of the Egyptian subjugation. But miraculously, the society has changed and now, even in exile, we are free to take Shabbos off from our work. The very concept of a seven-day week in the secular world is itself a miracle. The week is the only calendrical component with no clear astronomical significance. A day represents one full rotation of the earth on its axis. A year is one full revolution of the earth around the sun. But a week is nothing more than a group of seven days. The secular world could easily have chosen a six or eight-day week and that would have spelled eternal trouble for the Jews. (In fact, there have been a number of proposed changes to the calendar designed to maintain the same day of the week for each calendar day by using a “Worldsday” which would not belong to any day of the week.) On the day of Shabbos these miracles must be realized, in combination with the miracle of yetzias Mitzrayim.
Rambam, in Moreh Nevuchim, seems to concur with this approach. He writes that the two mentions of Shabbos in the aseres hadibros teach us two separate aspects of Shabbos. In parshas Yisro, we are taught why HaShem chose to sanctify the day of Shabbos and its significance in the days of creation. Here, in Va'eschanan, we are taught why it is that we must keep the Shabbos, namely, to remember the enslavement in Mitzrayim when we had no days off and appreciate HaShem's great deliverance of us from there.
Perhaps we can summarize simply: The ma’aseh bereishis aspect of Shabbos celebrates HaShem’s own greatness. The yetzias Mitzrayim aspect celebrates the greatness that HaShem chose to bestow on us as a nation.