One of the strangest exchanges that we find in baba kama is the dialogue about why the term "tov" is missing in the first of the aseres hadibros and is only found in the last set. R' Chiya Bar Abba then makes a comment indicating that he isn't sure about the proper text, until R' Tanchum confirms it. Finally the gemara concludes that since the first tablets were to be broken, Hashem foresaw this and left out the term "tov".
Rashi explains that the gemara is making reference to the term "tov" in the mitzvah of kibud av v'eim that says למען ייטב לך. The Maharatz Chiyus is bothered by the very difficult question, how is it that the Tanaim were not familiar with the text of the aseres hadibros, until it was confirmed by R' Tanchum. Although Tosafos in Baba Basra writes that sometimes they were experts in pesukim, it seems strange to say that they didn't know the aseres hadibros!
The Maharatz chiyus suggests that the discussion was whether the aseres hadibros that are recorded in parshas yisro was the text on the first set of luchos, and the aseres hadibros in v'eshchanan are the second set of luchos. R' Tanchum had a mesorah that it was in fact the case, to which the gemara finally explains that it now makes sense that the luchos which were to be broken didn't contain the term "tov".
The Torah Temima (Devorim 5:16) offers another approach. The gemara is making reference to a midrash where Hashem says to Moshe that He is going to give a second set of luchos, to which moshe is happy and responds "טוב לי תורת פיך מאלפי זהב וכסף". Why did he only respond this on the second and not the first? On that the gemara explains that since they would be broken, it would be inappropriate to say that about the first set of luchos.
However, based on the conventional understanding of the gemara, it certainly seems to hold that the aseres hadibros of yisro were the first luchos, and v'eschanan the second. Based on this, we can make another observation. In the second luchos, by shabbos and kibud av it says כאשר צוך ה' אלקיך which rashi interprets makes a reference back to mara where the water was bitter. Why is this reference specifically in the second luchos and not the first? The Chasam Sofer in Parshas Beshalach explains that Hashem taught us in Mara that he is our personal doctor - כי אני ה' רופאיך. Unlike a physician who just heals the sick, Hashem is our "family doctor" who is just as interested in providing us with preventional medicine, as He is with remedies for illness. In the second luchos Hashem wanted to remind klal yisroel that doing aveiros (such as the golden calf) forces him to bring upon us illness, and then show he can heal. He much prefers avoiding illness in the first place by our commitment to His Torah - כי אני ה' רופאיך