Well, I used Amsoil for years and have recently gone to Mobil 1. I can tell ya that I have done my homework on this issue and the main (if not the only) benefit to synthetic motor oil is in its reduction in friction. Conventional motor oil has molecules of varying sizes (from small to extremely large). With synthetic on the other hand all molecules are of uniform size and they are about half the size of the smallest of petroleum based molecules. Something like comparing a larger tertiary protein to an amino acid.

So for metal to metal contact the synthetic will penetrate better and drastically reduce friction and in my opinion it would be great for firearms in such applications. Where synthetic lacks adequacy is in its ability to displace moisture and prevent rust. In an automobile engine the oil pump is continually drenching it with oil, so this issue is not a concern. Rust prevention would be a weak point for synthetic in a firearm application, however.

In air rifles and paintball guns, petroleum based oils are a big no-no. Since both use a number of rubber o-rings, a petroleum based oil would quickly break the rubber down. My RWS air rifle gets nothing but RWS airgun oil. This can apply to modern firearms as well. Bear in mind that if there is any rubber seals, o-rings, etc on your gun anywhere, it should not be oiled with a petroleum based oil.