In the comic book, Superman has been shown to heal like Wolverine. Pretty much the only way to beat a Kryptonian is with Kryptonite, Magic or sending them to the Phantom Zone. Even when Superman died in the comics, he ended up going into a Kryptonian coma, where it looked like he had died (i.e., having no vital signs), but was healing. Also, Darkseid's Omega blast has been shown to hit hard enough to kill Kryptonians, as he one shotted Super Girl at the end of Crisis on Infinite Earths, and has knocked Superman unconscious with one hit.