Saitama's gag-character limitless power and the ability to end any fight in one punch gives him the edge.
This is a clash between a realistically portrayed superhuman and a satirical character designed to win every fight. Omni-Man is genuinely one of the most powerful characters in his universe โ FTL speed, planet-cracking strength, and millennia of experience. In a conventionally written fight, he would be a formidable challenge for almost anyone.
But Saitama exists as a narrative concept: he is the character who wins. His power is literally defined as being beyond whatever his opponent can do. In the manga, he has shown feats including punching through a planet-destroying attack, time travel through sheer punch power, and zero-diffing a cosmic-level threat. His serious punch generates more force than anything Omni-Man has tanked.
Omni-Man's experience and ruthlessness are real advantages, but Saitama's durability feats include tanking attacks that would atomize Omni-Man. The satirical nature of One Punch Man makes this difficult to judge by conventional power scaling, but taking both characters at face value of their feats, Saitama's ceiling is simply higher.
Omni-Man has millennia of real combat experience, fights at FTL speeds, and has helped crack a planet. His ruthlessness and Viltrumite physiology make him one of the most dangerous warriors in fiction.
Saitama's power is narratively limitless โ he exists to end fights in one punch. His serious punch has demonstrated force beyond planetary destruction, and he has tanked attacks that dwarf Omni-Man's best feats without any damage.
Saitama wins through his narratively limitless power ceiling. Omni-Man is genuinely powerful by conventional standards, but Saitama's feats in the manga place him beyond what Omni-Man can survive.
Omni-Man also fights
Saitama also fights