This is really simple--there is only one version. The Ten Commandments are listed twice: in Exodus 20 and Deuteronomy 5, but they are the same. Exodus 34 is not a second list of commandments (there's no list!), it's simply a renewal of the Covenant that God made with the nation of Israel. The reason this renewal was significant was because Moses had not yet reached the bottom of the mountain with his fresh set of tablets before he saw the israelites worshiping Jehovah by means of a Golden Calf (that's breaking the second commandment).
The article "Which Ten Commandments?" that you referenced is misleading: Catholics and Protestants DO have separate versions of the Ten Commandments, but only because Christians read the Ten Commandments from the Bible, and Catholics read it from their Catechism, which is derrived from, but not the same as the Bible's account. There is no difference between the Jewish and Christian versions of The Ten Commandments because they both read from the Hebrew text, or an English translation of the Hebrew text in the Pentateuch.
Another important thing you don't seem to know, is that (for judaism/jews) these commandments are just 10 commandments in 613. They're not really more important, they're just the first (and the only) ones that were spoken to all of the people. What was referred to, by saying that commandments are on a historical basis for US law, may be more about these 613 laws, not just the 10 you referred to. You can look at http://www.jewfaq.org/613.htm for example. Please read the Talmud to see what they really meant with 'law'. And as the previous poster said, there's just one version. The link you put is silly in the sense that it places catholic, protestant and hebrew versions as different but parallel things. That's not right. All the versions are derived from the original one, the hebrew version. That's the incompetence of the scribes that made them different.
Many people hate dubbed films, so why do people argue on transcriptions of transcriptions of transcriptions? Read the original (or at least the oldest version)!# anonymous