King Vegeta is >19 Zettatons, whilst Superman is 5.0811706477439e+30 Joules, I have... absolutely no idea how to convert that into Zettatons, I'll let someone else do that for me.
Superman absolutely man-handles King Vegeta in Lifting Strength, Class Z to King Vegeta's unknown, it sounds to me like if Superman gets him in a grip it might be pretty much over (depends on how large that AP Gap is.)
Superman also appears to have the edge in versatility, he has heat vision, energy projection similar to King Vegeta, force-fields, and freeze-breath. Superman also has regeneration to keep him in the fight longer.
King Vegeta has (maybe) greater experience, (definitely) greater combat skill, and potentially turn himself into a Great Ape. (Assuming he can also create an artificial moon, which I wouldn't put past his capabilities.)
Great Ape Vegeta though, if worse comes to worst, is an entirely different animal. While I wouldn't put it past Superman to figure out that his tail might be the source of all those blutzwaves, it'd be dealing with him and getting to that tail that would be the hard part. Depending on whether or not King Vegeta one-shots, Superman might either play it safe and spam-grapple King Vegeta to victory or try and wear him down with forcefields and such.
With all that said and done, I'm gonna give it to Superman hard-diff. His versatility and far greater lifting strength I feel might overcome any of King Vegeta's advances. Larger Ki Blasts potentially get blocked by force-fields or dodged, any physical confrontation has a risk of King Vegeta getting grabbed, and even if he is getting overpowered Superman's freeze breath could come in handy. King Vegeta hasn't shown to resist cold on a level that could freeze the surface of the Sun, so that could be an incap.