You would be correct Almalexia.
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If you already have stat caps without a weapon then I still think Giantsgall is bette since there plenty of melding options and you can reorganize your gear to even further better yourself. I don understand why having another meldable option is bad, add in some ACC on top of that and the weapon is looking pretty good. I think you just aren't thinking outside of the box, there is always a way to better yourself and opening up more oppurtunities is never a bad thing. Basically Giantsgall adds far more flexibility then Ifrit/Moogle.
Your accessory slots are a lot more flexible than the weapon slot.
Mogfists all the way if you aren't going to be using GC gear.
Mogfists > Ifrits as well. You can wear a +30 Atk necklace. But you can't wear a +30 Accuracy Necklace.
So yeah, basicially Relic>Garuda>GC(with gear bonus)>Moogle>Ifrit>Skirmish
I would be interested to know what your accuracy is, and what damage modifying stats you are missing to get your accuracy. It's true that Monk has natually high accuracy WS's, but if you're under 95% then you're too low. (Aim for 100%)
Unless your accuracy is 95-100%, then accuracy>damage
Ifrits Claws + Explorer's Choker(Atk + 30, Acc +15)
Moogle Fists + HQ Electrum Choker (Atk + 30, Acc +30)
Don't forget that DPS is a damage modifier as well.
Relic>Garuda>GC(With 5 Piece Bonus)
I love Monk on Garuda. Easily a very strong asset to the fight.