That link works for me.
So, according to the profiles…
Omni Man has an AP of about 347 Megatons. Nanoha has an AP of 993.6 Megatons. Nanoha has the ap advantage, by about 3x.
Looking at their kits, Nanoha has things like Information Analysis, Telekinesis, Healing, and Forcefield Creation, whereas Omni-Man appears to have a lackluster Regeneration and Shockwaves. Nanoha has the Ability advantage here, it seems.
Omni-Man has a class M Lifting Strength with a calc of 1.86*10^7 Kilograms, which appears to be about the middle ground of Class M. Nanoha has a Class M LS with no calc, so we’ll assume Baseline. Omni-Man has the LS advantage.
Omni-Man has combat experience going back thousands of years, which appears to dwarf Nanohas skill feats of learning Magic at 9 and being a Tactics Instructor. Until advised otherwise, I assume Omni-Man has the Skill Advantage.
Looking at Stamina, Nanoha is rated at Superhuman for use of a self-damaging system excessively, but Omni-Man is capable of going fight after fight after fight without tiring, holding his breath for up to two weeks, and sustaining injuries constantly without growing exhausted. It appears Omni-Man has a Stamina advantage.
For range, Nanoha has access to dozens of Kilometers via her Magic, and Omni-Man reaches a maximum of hundreds of Meters via a Shockwave. Nanoha easily has the range advantage.
With all that said, honestly, I think this fight’s skewed in Nanohas favor. She has a far more advanced kit, range that beats out Omni-Mans by the thousands, force fields to keep him from ever actually landing a solid blow, and If that wasn’t enough, almost triple Omni-Mans AP. The only Wincons I see are Omni-Man outlasting Nanoha until she’s exhausted while simultaneously managing to not get knocked out himself, or somehow restraining her with his LS advantage.
Of course, I don’t know enough about either character to properly analyze their starting moves. If Nanoha doesn’t do what her kit seems like she’d do, and actually goes for Melee Combat, I believe Omni-Man has a pretty good chance- holding a clear Stamina and Skill advantage over her, and a higher LS does wonders. The main problem seems to be Nanohas incredible Range and Omni-Man’s saddening lack of it.
tl;dr I am not experienced with either character, to be perfectly honest. However, going by their profiles alone, I believe Nanoha holds a clear advantage over Omni-Man due to her Range and AP advantages, If not to the point of just kind of being unfair.