There are a number of hints that the Ultima Weapon, and the Ultima spell, are both direct manifestations of Zodiark's power / will. This is arguably because the Heart of Sabik, implied to be some manner of Dark Crystal, acted as the Ultima Weapon's core.

Quote Originally Posted by Hydaelyn
Thy foe is Darkness clad in steel.
Quote Originally Posted by Lahabrea
... [T]he hammer of Darkness must needs be brought to bear upon the shield of Light.
Quote Originally Posted by Lahabrea
Behold but a sliver of my god's power!
As such, directly resisting Zodiark's power on the corporeal plane would be difficult for the already-weak Hydaelyn. Ultima is an extremely powerful spell, implicitly a direct manifestation of Zodiark's power - so it would stand to reason that it would take an equal or greater amount of Hydaelyn's energy to protect us from it. With very little strength left and even less after protecting us from Ultima and helping exorcise Lahabrea from Thancred, She has been unable to communicate with us often since.

With few details on Omega, none can yet say if it is as anathema to Hydaelyn as Ultima (Weapon) was. It does possess more power and destructive potential (wrangling Bahamut and going toe to toe with Shinryu vs. fighting the likes of Ifrit, Titan, and Garuda), but without knowing if it has a core akin to the Heart of Sabik (Darkness) powering it...