This is one true case of: 'I don't know who'll win', because I don't think there's been even one case where Aqua's true power has been witnessed, she just does things on a whim even if it causes massive problems, but even then she's always doing stuff just to show off and not seriously. Considering she's also a goddess (albeit a pretty dumb and 'special' one) it's never shown how powerful she truly is despite being feared by most high-profile enemies (or simply annoying them).
But we've witnessed Ainz' power and the extent of it, coming mainly in the form of 'cash shop items' and his high level. But considering they both exist in different universes with different parameters, it's kind of difficult to know who would win, the only thing both characters have on comparison is their ability to resurrect dead people quite easily, like it was a trivial favour.
By my rough estimation, it seems like Yggdrasil levels are worth basically half of what a 3.x edition D&D/Pathfinder character would have, so at level 100, he's like a level 50 epic character that could easily challenge the "physical gods" of the Olympian pantheon from 3.x edition.
Aqua, meanwhile, may be a goddess, but she's objectively all but useless in a fight.
Also, Turn Undead depends upon edition, but it's generally based upon hit dice of the undead, and you need to be pretty high level to affect a 50HD undead.
By my rough estimation, it seems like Yggdrasil levels are worth basically half of what a 3.x edition D&D/Pathfinder character would have, so at level 100, he's like a level 50 epic character that could easily challenge the "physical gods" of the Olympian pantheon from 3.x edition.
Aqua, meanwhile, may be a goddess, but she's objectively all but useless in a fight.
Also, Turn Undead depends upon edition, but it's generally based upon hit dice of the undead, and you need to be pretty high level to affect a 50HD undead.
Comparing between systems just doesn't ever work, and it's never more clear than a comparison between pathfinder and the overlord world. For one, power plateaus in Pathfinder at higher levels. A level 20 character would turn a level 10 character to mush. A level 20 character on the other hand is still a major threat to a level 30 epic character. The same can't be said, I'm pretty sure, between a level 33-66 and a level 66-100 character in the Overlord world. There are other problems with this measure.
Shalltear used unlimited regeneration (fast healing in pathfinder terms as she can be killed whilst regeneration is active) by killing minions. Whilst this is excellent in a MMORPG where sustain is important, in a game like pathfinder healing is often seen as a wasted action as every time she summons minions and heals she will be subject to enemy spellcasters or melee characters that would tear her apart. If vampire weaknesses carries between systems, then Shalltear needs to fail a single save against a solar beam (level 7) or solar flare (level 8) spell before being reduced to ashes instantly. Action spent recovering HP are actions that the enemy can use to rain save or die spells. If weaknesses don't carry over then resistances and immunities shouldn't either, which means that people can just spam holy word or weird at her until she drops, her regeneration and health pool be damned. Not exactly impressive for what is meant to be a CR50 encounter. The ability to heal an unlimited amount is also something remarked as exceptional in the Overlord world, where in Pathfinder it is one of the most trivial and common monster abilities.
In the fight with Shalltear Ainz cast what is effectively a series of wish spells. That is a spell considered so powerful that it was a limited item, a major artifact in pathfinder terms, in order to get his win. With some trivial optimization, sorcerers at level 20 in pathfinder can cast wish 7-8 times per day. He used what is effectively quicken exactly once, again something that any half-baked level 15 mage would have access to. The Overlord world appears to have a lot of AOE mass-murder spells, but 1v1 the fights that are shown is not the fight between what are effectively god-tiered characters.
Aqua, meanwhile, may be a goddess, but she's objectively all but useless in a fight.
Only because she's too dumb to realize that water-based attacks are useless against enemies who resist or are immune to water damage, like giant frogs.
She's still a goddess, though, and because of this her Holy element attacks are overwhelmingly effective against undead. She's able to easily curbstomp Ainz (and manages to OHKO Shalltear!) and the only reason she doesn't is because Kazuma stopped her.
Theres also the problem of them being from different universes I assume the rules if their individuals worlds are at least a little different so any decision of "who would win" can't really please everyone. Just like every "who would win" ever.
Lets be honest - There's one course of action that is 100% sure here. - Aqua will be Aqua and do alot of dumb shit. - Ainz will almost murder her on the spot. - Kazuma will interfere and start scolding her for any kind of reasons, realy. Also he would demand from Ainz to stfu and do not interfere. - Ainz will get bored, shrug and go away doing his things.
Got two out of four for how their first encounter went. Ainz rather stupidly decided to tank Turn Undead because it was "Low Level". As others have mentioned... Aqua's damn effective at dealing with undead. Yes, they actually met in Isekai Quartet.
This is why Memes aren't useful in a serious discussion.
Aqua might be an imbecile, but she's also a powerful support cleric who, as a goddess of Healing, means she's designed to be almost *exclusively* good against undead.