I think it depends on the writers. A lot of their fights begin with Darkseid winning, then Supes goes all out and "wins" (one can never really win against Darkseid - unless one is Batman).
I mean, look at these 2 fights:
There's
this one where he can baerly survive against him until he goes rage mode/absorbs some more sun rays, and then barely "defeats" him with Supergirl's help.
Then there's
this one where SUperman gets trucked, at first. Then after Batman does some awesome stuff (because, y'know, he's Batman), Superman comes out of nowhere and hands Darkseid his shit on a silver platter.
I don't think we can ever decide which of the 2 is greater. It depends on what's going on in the story, who Superman has on his side, etc. For the most part, I think they're evenly matched, but there are times when the odds bend heavily to one side or the other. I think, like I said, it just comes down to the writers.