Omni-Man's planet-level power and FTL speed are far beyond what Wolverine's healing factor can sustain against.
Wolverine's adamantium claws can cut anything, and his healing factor makes him nearly immortal. But Omni-Man fights at a power level that makes these advantages insufficient. A Viltrumite who can crack planets generates enough force to scatter Wolverine's adamantium skeleton across a continent.
Wolverine's healing factor has limits โ he has been killed by being fully submerged in adamantium and by having every cell in his body destroyed simultaneously. Omni-Man's attacks approach that level of destruction. A full-speed Viltrumite punch could potentially separate the adamantium skeleton from the biological tissue that regenerates.
Wolverine's claws could theoretically cut Omni-Man's Viltrumite skin, but Logan would need to actually land a hit on someone moving at FTL speeds. The speed differential makes close combat nearly impossible for Wolverine.
Omni-Man's FTL speed prevents Wolverine from ever landing a claw strike, and his planet-cracking punches can overwhelm the healing factor by destroying Logan's body faster than it regenerates.
Wolverine's adamantium claws can cut Viltrumite skin, and his healing factor makes him functionally immortal. His centuries of combat experience and berserker rage make him relentless regardless of the opponent's power.
Omni-Man wins through overwhelming speed and power. Wolverine's claws are dangerous in theory, but FTL combat speed prevents them from being relevant. The Viltrumite's attacks also exceed the healing factor's recovery rate.
Omni-Man also fights
Wolverine also fights