Chazal tell us that before Hashem gave us the Torah, he offered it to the other nations. "What's in this Torah?" asked the bnei Eisav. When Hashem told them that it contained a command not to murder, they turned it down. "Our grandfather was told, 'Al charbecha tichyeh,' so how can we accept a Torah that prohibits murder?" they replied. Hashem went to Amon and Moav, but they too turned down the Torah because it prohibits arayos, which is part of their culture. And so each nation had its chance, but in the end, we alone were the only ones willing to accept the Torah.
Question: murder, arayos, etc. are all among the mitzvos bnei Noach. Eisav, Amon, Moav had to observe these commandments irrespective of whether they accepted the Torah. What did the nations hope to gain by not accepting the Torah? Or, to rephrase the same question, how would kabbalas haTorah have changed their obligations?
I want to present two answers I saw and one that I thought of:
1. The scope of mitzvos is different: In the dictionary of an aku"m, murder means killing another person. Yet, for a ben Torah, murder goes far beyond that. Someone who embarrasses his friend, malbin pnei chaveiro, is guilty according to Chazal of shefichus damim, murder. The same expansive scope is true of arayos, theft, and many other mitzvos. You don't have to walk into a bank and hold it up to be guilty of gezel -- if you just wake someone up too early you have committed gezel sheinah. This is what the nations of the world were rejecting (see R' Nevenzah's sichos where he quotes this from Kelm mussar).
2. Mitzvos bnei Noach are about the law; Torah is about a relationship with G-d. The Netziv in the beginning of Parshas Bechukosai offers an analogy: a doctor prescribes a regimen for good health to a patient; he prescribes the same regimen to his son. However, the doctor does not just tell his son what to do like any other patient and leave it to him -- the doctor in this case wants his son to follow his direction, he wants him to obey and be healthy. The benefit to the son of following the doctor's advice is not just good health, but it is a stronger relationship with his father who is doing the prescribing.
Following the mitzvos bnei noach ensures the good health of society. Following the Torah ensures the good health of our relationship with G-d as well. It was that relationship that the nations rejected.
3. Torah is a culture, not just a set of laws. What Eisav and Yishmael and the other nations were telling G-d is that their culture is one of bloodshed, theft, arayos, etc. The ben Noach laws for them are a brake that forces them to curb their natural instinct, to hold back from being barbarians. That's not what Torah is all about. As the Rambam writes in Shmoneh Perakim, the goal of Torah is transform a person into someone who does not desire bloodshed, or theft, or other crimes -- not simply to avoid acting on those base desires. The goal is to cease being a barbarian, not simply to cease acting out like a barbarian. The nations could not envision changing in that way.