I don’t think his C-staves is that big of a deal, nor is it notably important.
Both can do the same job for most of the game. Use Heal and Torch.
You don’t need Restore unless you go B route, and only in Ch14. Ch16 warrants its use but this is way too late for initial staff rank to be a notable factor.
You don’t get Barrier until 12A or 13B.
Recover isn’t necessary as Mend is sufficient for the whole game, if you do need it it is in Ch14’s secret shop on both routes.
Both Natasha and Moulder will have C-Staves by then, regardless of which you use. Moulder has extra staff rank, but you don’t need it for that part of the game.
Rescue requires saving the NPCs in Ch17, it can have niche uses in certain maps afterwards.
Sleep and Berserk are incredibly hard to obtain in non-JP versions, Silence has so few targets it is mostly worthless.
Warp is useful; Moulder needs little investment to hit A-staves. Natasha can hit it without too much effort as well, as you have plenty of time to spam Barrier or Torch in the maps before you even get Warp.
Fortify is overkill and not usually used, Latona is powerful but shouldn’t be needed unless something goes horribly wrong.
As such, most of the game’s staff usage boils down to Heal/Mend to keep units alive, Torch to deal with FoW and Recover to deal with the few status staff users and Stone Gorgons.
Both can do the job without any real investment beyond using them to do their job. Warp is arguably the only staff that seriously warrants consideration given its rank requirement and obtain time.
As for their performance outside of initial staff rank, Natasha is arguably slightly better, counterintuitively.
Natasha’s biggest advantage is not her growths or her alternative promotion to Valkyrie, but her 6 base LCK.
Natasha joins with 18 HP and 2 DEF; low, but you’d be hard pressed to find anything that can kill her in one hit for a few maps, surprisingly. You can safely expose her to a Javelin or even a Hand Axe for the most part with just her bases as she can survive it without issue. Moulder on the other hand, risks getting crit by basically everything, meaning putting him on the frontlines is very unsafe, and his head start and difference of 2 HP is way too low of a margin to be notable, especially as the first Guiding Ring is liable to go to Artur or Lute.
Natasha will overall do a better job of not dying on the frontlines due to not facing crit, and still being able to take a hit for the most part; by the time her bulk comes into question, Guiding Ring #2 is on its way and is enough to patch up the problem.