If the main justification for Irene's victory is going to be the idea that non ds magic can't harm dragons, then I wish people would actually provide a page in which that was established. The only basis for this idea that I've seen is the inability of Tenrou Fairy tail and GMG Jura, Kagura, and Lyon to harm dragons which is completely irrelevant given the change in power since then.
This is the same as people assuming August is suddenly a Dragon Slayer. That's the only way he beats dragon Irene. August > human Irene most definitely, but dragon Irene is a whole other level. August might be able to copy the elements but how exactly is he copying the lacrima?
All we know is that Brandish hyped them up as pure equals. There is no sufficient evidence for any other assumption. My main point was that if you want to use Brandish's quote then you also have to use Hiro's quote at the beginning of chapter 525 that says August is the strongest of the Spriggan 12.
This is the same Brandish that also admitted to not being close to Irene. In fact iirc Irene mentioned not seeing her in years. August by comparison practically raised Brandish and lived with her in Alvarez so i'd think she would know more about what August is capable of than Irene. Also when she was talking to Lucy and co. about August she specified August being the strongest
male, and this was going off of her little knowledge of Irene. You can even assume what she knows of Irene comes from August himself, and we can use the example of him having to tell her about Irene's compression magic after U1, as I doubt when they met before it was in a battle situation.
As
@natsulucy mentioned when Irene and August met again, she did specify yielding to him only to let him save face presumably in front of Brandish as the general, but as "arrogant" as she is she has shown to give respect where it's due as per her interactions with Zeref, Acnologia, and even August and she's never really shown to overhype herself.
Saying August can enchant Irene out of her dragon form is the most presumtuous thing i've seen in this match up. How exactly would he do that? As stated before he wasn't there when Zeref did it for Irene the first time. Unless of course Zeref wandered around enchanting random humans out of their dragon forms with August trailing behind him, I don't see when he would have had the chance to copy that specific enchantment. Also, Irene has been shown to use her staff to perform her atmospheric enchantments such as when she changed the climate of Mount Zonia and also when she was fighting Acnologia so it's safe to classify those specific examples as holder type magic which August can't copy.
If Irene's sage mode is to simply amplify as
@MonkeyD-Dragon states, then it's safe to assume she uses True Heavenly Body Magic in general, so this would include meteor i'd imagine. Since a few people here have the argument "August blitzes her with meteor" is that really the case I wonder?
I'm not so biased that I wouldn't give this fight to August IF there was proof that he is capable of using DS Magic. As it has not been proven Irene definitely takes it. Her MP in dragon form would surpass August' MP so even if he somehow copied her amplified spells it still would not be on the same level, so Irene beats him in raw power.