Ainz wins due to hax. It is specifically stated that he was one of the few players who mastered using delay spells + timestop to ensure the opponent has no time to react, and even if that doesn't work the first time, he could just use timestop and place [True Death] Spells in all directions, making it impossible to dodge. He can presumably also use a delayed [Reality Slash] if instant death somehow does not work.
If all else fails, [Cry of the Banshee] and [Despair Aura V] both have an AoE effect and cause instant death as well. He could also simply use [Death], which is targeted and undodgeable like [Grasp Heart], but causes instant death without needing to physically harm Saitama. Any way you look at it, Ainz wins.
Even if he doesn't get the drop on Saitama, as soon as the fight starts, he can just use time stop or [Invisibility] + [Perfect Unknowable] to completely erase his presence and then use [Death].