Blade: Yu and Aeolian Edge both have secondary mobs of 28% DEX 28% INT, so WSC for both weaponskills is the following.
WSC = floor(0.85*floor((999*0.28)+(999*0.28))) = floor(0.85*floor(559.44)) = floor(0.85*559) = floor(475.15) = 475
The systematic factors for both weapon skills is the regular dINT which will be capped at 32. Blade: Yu has a constant fTP multiplier of 3.00 (more TP = longer Poison) while Aeolian Edge is 2.75 3.50 4.00. Thus the damage before atma and magic attack bonus are applied will look something like this.
Code:
Weaponskill TP 100 TP 200 TP 300
Blade: Yu 1733 1733 1733
Aeolian Edge 1591 2016 2300
If you happen to have the elemental obis/gorgets (which are best in slot for any weaponskill under brew), then it looks like this.
Code:
Weaponskill TP 100 TP 200 TP 300
Blade: Yu 1846 1846 1846
Aeolian Edge 1704 2129 2413
The next step is to evaluate gear and Atma. The only thing that you can do besides the elemental obis/belts gear wise is MAB equipment. Transcendancy grants +900 MAB, thus reducing the benefits from additional MAB to 1/10th of what it normally would be. There is little MAB gear available for NIN anyways, so I'm just going to ignore it for the sake of comparison (it's honestly not worth worrying about.)
For Aeolian Edge, Martial Knife is your best bet. It increases the damage by quite a bit as you'll start out at the TP 200 spot on those tables. The best Atma is Atma of the Gales, it adds 30% wind potency to your spells and weapon skills. The next best is Atma of the Smiting Blow. It gives you another 100 TP bonus that stacks with Martial Knife. There's not much else for Atma, Atma of the Ultimate is a distant 3rd place (+50 MAB +50 MACC.)
For Blade: Yu, the best Atma are Atma of the Noxious Fang (40% water potency) and Atma of the Tusked Terror (20% water potency.) This is followed distantly by Atma of the Ultimate. The best weapon is the magian katana that gives weapon skill damage +10%, but I don't even think a single person ever bothered to get this.
Damage tables for this are as follows (weapon skill damage +10% not used for this.)
Code:
Weaponskill TP 100 TP 200 TP 300
Blade: Yu 29113 29113 29113
Aeolian Edge 21716 27518 31395
Code:
Weaponskill TP 100 TP 200 TP 300
Blade: Yu 31012 31012 31012
Aeolian Edge 23259 29060 32936
There's also one last thing to be said about these weapon skills. Aeolian Edge has three different skill chain properties and is capable of creating a skill chain with itself. It can do this indefinitely (scission > detonation > scission > detonation etc.) Blade: Yu, although I haven't used it since I brew mainly on Thief, I think is capable of doing Induration > Fragmentation, although I'm not completely certain. Either way, these skillchains can contribute a lot of damage if they're unresisted.
These numbers may be off a little bit on normal mobs due to where I truncated numbers, but they will be very close (within a fraction of a percent.) You won't see numbers that big on Rani because caturae have some MDB or MDT-% trait and Rani also builds damage resistance. However, I was able to casually kill it with Aeolean Edge after waiting a while to proc (I didn't have the right atma on either because I was tanking.) So I don't think that it will be a problem. If Rani resists water (Blade: Yu is water based), then you may not be able to use that weaponskill.
As far as strategy goes, this is what I recommend. When you're done procing, keep on fighting it regularly until it weaponskills then immediately use your brew and start spamming. The reason for this is you want it to die fast without accumulating TP, or you could become charmed if you're unlucky when it gets down. Turn around while it's casting so you don't heal it. Forget about using Evisceration, it's really not worth the effort and you don't want to be giving it TP anyways. Really though it should only take 4-5 WS to kill it if you have a good set up for one of those weaponskills.