So first start with the chasam sofer It is on the left hand column of that print. He starts with the statement in the Gemera that there is nothing that is forbidden to non-Jews that is permitted to Jews. He then goes through different problems which would seem to contradict that, explaining how the Talmud answers the ones it does bring up, and goes on from there.

The problem is that the Rambam himself says that there are things that are permitted a Jew but forbidden to a non-Jew - namely some forms of a limb from a living animal - Malachim 9:13

The Chasam Sofer attempts to deal with this question, but only half of it - how can a Jew be permitted the meat while the animal is still convulsing after the Shechita. But in Maachalos Asuros 5:1 he says this prohibition is only concerning Kosher animals, but for non-Jews in Malachim 9:13 he says it is forbidden for all animals for non-Jews.

He then says that non-Jews are not punished for birds, but limbs from living birds are forbidden to Jews.

What is particularly surprising is that he doesn't address this question, nor does he deal with the Rambam's specific language of " ויש שבני נוח חייבין עליו, ולא ישראל" - there are things that a Ben Noach is obligated on, but not a Jew. The Rambam is all but disavowing that the Halacha is that there can't be anything lenient with a Jew.

It seems quite obvious that he doesn't hold of it as the Halacha.

With difficulty you could answer this question that it is forbidden to a Jew for different reasons, and this seems to be the Chasam Sofer's approach - as long as Jews are more limited it doesn't matter why. But that doesn't really address what the Rambam is saying, it reads something else into what he says.

Next question: The Chasam Sofer says that the Rambam's source for the idea is Nedarim 31a. The discussion there is about someone who makes a vow referencing all those who keep Shabbos.

The Talmud says the reason this includes only Jews and converts is that they are commanded in Shabbos

But non-Jews "do it but are not commanded." Which, the Chasam Sofer says, implies to the Rambam that they are not obligated, but not forbidden. Why in the world not?? How can you read such an implication and create such a Machlokes between two Suggias?

More importantly - The talmud in Nedarim is talking about Idol Worshipers, not Ben Noach! So then what is the basis for saying a non-Jewish Idol Worshiper is forbidden from keeping Shabbos?

The entire context of the Talmud there makes no judgement about whether the non-Jew is doing a good thing or a bad thing, but rather discussing what a person means when he says "those who keep Shabbos." He doesn't mean non-Jews because they have no obligation to (that is the conclusion) even if they happen to. This is not a normative statement about non-Jews keeping Shabbos.

On the contrary, if it said they are forbidden it would have muddied the point. There is simply no Diyuk in the Gemara, or in the Rambam, to justify this.

I could go on and on with this, but I'll leave off with two points. One, is that the Rambam in Malachim 10:9 says: אלא או יהיה גר צדק ויקבל כל המצוות, או יעמוד בתורתו ולא יוסיף ולא יגרע. ואם עסק בתורה, או שבת, או חידש דבר--מכין אותו ועונשין אותו, ומודיעין אותו שהוא חייב מיתה על זה; אבל אינו נהרג. - A non-Jew has a choice - convert or be a Ben Noach and don't add or subtract anything from the 7 Mitzvos - which he then details the punishment (or lack thereof) for

keeping Shabbos or learning Torah or creating new religious practices.

To read it the way the Chasam Sofer reads it, there is no problem for a Ben Noach to make entirely new religious practices and holidays. This lacks any source or reason.

The next thing is that it is the common practice to require a non-Jew to violate Shabbos in some minor way while in the conversion process. Some don't require this on the theory that just a non-Jew is allowed to learn Torah with the intention of converting he can keep Shabbos with the intention of converting. Either way, we see the Halacha is not like the Chasam Sofer here.

I think the correct reading of the Rambam is that גוי - saying Goy or Akum or whatever the version says, is the more inclusive term (I'd like to see a counter example). When he says גוי, he means everyone. When he uses Ben Noach it is because he is talking about a non-Jew who has separated himself from the group by keeping Mitzvos.