The main reason is that they are both descendent of Abrahamic based religion that always slaughter their herd animals to eat by the name of one God. Muhammad is a descendent of Ismail while Moses is the descendent of Isaac, both are siblings from the same father Abraham but different mother. Even the original languages for their holy scriptures namely Arabic and Hebrew are very similar by being rooted from the same original Semitic based language.
But like another commenter pointed out, interpretations of these rules vary widely among practitioners so making blanket statements about who might eat what is difficult.
OK I will re-phrase that to "one of the main reasons" since for the meat to be considered halal it needs to fulfill two main requirements. Firstly it must be slaughtered by the name of one God and secondly it must be slaughtered with proper procedures. For most religions, the practices are always come down to spiritual and physical aspects, and as you probably can deduce that the first one is the spiritual aspect of it.
Having said that, Quran refer to the Jews and Christians as "People of the Book"[1], and that's the main reason some of their rulings are acceptable in Islam. Another fun fact is that "Moses" is mentioned by name more than any other prophet names including "Muhammad" inside the Quran [2][3], and there is also one Chapter "Mary" referring to the Jesus' mother.
[1]https://en.wikipedia.org/wiki/People_of_the_Book
[2]https://en.wikipedia.org/wiki/Moses_in_Islam
[3]https://en.wikipedia.org/wiki/Prophets_and_messengers_in_Isl...
Under the strictest rules for each, halal meats cannot be kosher and vice versa, because the slaughter must be carried out by a member of the religion. The physical requirements for the initial slaughter are essentially identical. But it's not uncommon for Muslims to view kosher meat as acceptable, at least as an alternative (and there's scriptural basis for this).
The reverse really isn't possible because there are more restrictions on how kosher meat is handled after slaughter , most notably the removal of certain fatty tissues, nerves, and veins. More info on that here: