Saitama's gag-character invincibility is literally designed to beat anyone — but Superman's feats are more concretely defined.
This is Goku vs. Saitama all over again, but with DC's heavy-hitter. Saitama is a joke character whose power is 'wins in one punch' — that's the gag. Superman is a traditionally-scaled character whose power is enormous but finite and documented.
Superman has more impressive concrete feats: bench-pressing the Earth for five days, surviving supernovae, moving planets. Saitama's manga feats are catching up rapidly — sneezing away Jupiter's atmosphere, punching through a galaxy-busting attack — but are still arguably below Superman's peak showings.
The philosophical problem is the same as with Goku: Saitama exists as a meta-character who cannot lose in his own narrative. His power isn't 'very high' — it's 'whatever it needs to be to win instantly.' That's a fundamentally different kind of power than Superman's, which has been extensively quantified.
In a crossover written by a neutral author, this fight would likely be written as a stalemate or comedic outcome. Neither character can really 'lose' without fundamentally breaking their core concept.
Saitama's entire character concept is invincibility. His serious punch casually countered an attack that would have destroyed the planet, and he's never once shown any sign of effort or strain against any opponent. His power exists outside normal scaling by authorial design.
Superman has more documented feats at higher power levels and has been consistently written as one of the most powerful beings in all of fiction for 85+ years. He's survived forces that would theoretically exceed Saitama's demonstrated output. Superman also has versatile abilities — heat vision, freeze breath, flight — that Saitama lacks.
We're giving Saitama the most marginal of edges because his character concept is literally 'unbeatable,' but this is effectively a tie. Superman's concrete feats may be higher, but Saitama's power is undefined by design. The honest answer is that this fight has no meaningful winner.
Saitama also fights
Superman also fights