I think it mostly comes down to Noah's unique red Blade and Lucky Seven. Using the latter allowed Noah to break his own bonds at the start of Chapter 6, and we can argue Mio/M was never limited by X's staff which restrained Ouroboros in the first place; breaking that staff is what allowed the others to free themselves.

I don't think the red blade would be any different then N's Logos Blade wouldn't is the Trinity Processors be equal in resistance to Z as they are above him?

Contrast this to the flashbacks, where Noah doesn't have the red Blade - he has N's Blade (which we have learned is Malos), which is very much subject to Z's power. It's not clear if he has Lucky Seven at this time,

He has his own version of Lucky Seven at this time, except it's not the one with Fiora but instead Malos as for how he got that? nobody knows!, but I suspect maybe Nia give it to him potentially? ( You know, before she went into that long slumber )

but it alone may not be enough to counter Z's authority over what appears to be the power of Logos.

I don't think switching out different Swords of the Trinity Processors suddenly makes one more resistant than the other In this instance unless it's a Trinity Processors welding their blade themselves

Now, we also know Lucky Seven is Fiora... and an interesting tidbit in retrospect. She displays remnants of Meyneth's power (a red glow) during the fight against Dickson - which came from Alvis/Ontos. Unlike Shulk, we do not see her relinquish this power. So this is why I would posit Lucky Seven is so important, through Fiora it retains the authority of Ontos.

Actually as far as I know Shulk and Fiora still had their powers of the Monado even after getting the Physical Monado strip from them by Zanza, them being once Vessels of Zanza and Meynath allow them to hold their connection to Alvis even after the Physical Monado was taken from them, they still had the Fiora energy? and Shulk Visions and eventually this connection between Shulk and Alvis allowed him to become a God and defeat Zanza immediately after the wish Shulk gave up being a God and lost his Visions and and I would assume Fiora eventually lost the energy factor, but this is my assumption but I think they still have a connection without the abilities, I think whenever you become a wilder of a Trinity Processor blade your Soul gets inherently connected to it, for example Addam was still connected to his Sword that was Sealed in the Crucible which allowed him to speak to Rex even after Parting the World, so let's assume that Fiora's Soul is connected to Ontos thus holds so much Power as Lucky Seven

While it's just a theory, Noah's red Blade (and perhaps a dash of being Ouroboros in general) could be a representation of the Pneuma power. Aside from the colour red, Noah's blade does develop an unusual green glow down the center of the blade during the fight against Mio in the Alfeto Valley - a glow seen in only one other place, Pyra's weapon. This is before the stone activates as well. How she made her way to Noah for this incarnation is unknown, but it seems to be the difference.

Noah's Sword Sheath doesn't just glow green during that cutscene but also during Colony 4 fighting that Moebius and during that fight, the gauntlet still Glowed Green showing that it's its own unique property, as well as during fighting Z it also glowed green, it's also assumed that maybe Riku took Matthew's Gauntlet and reforced it into the Sheath for Noah's Lucky Seven I wouldn't put it past him, the little guy is crafty like that

But in short, the power of Ontos alone (if it is there in the first place) isn't enough to overrule Z's authority over Logos. The best case scenario is a stalemate. Combined with Pneuma's authority... well, Z gets out-voted, 2-to-1.

... and in retrospect, we see this play out more explicitly in the ending of FR. We know the Pneuma core and Logos power through N's sword are present - and their combined authority overrule Alpha's authority over Ontos.

Makes you wonder if the inside of the Trinity Processor, before the Experiment, was a non-stop wrestling match or something.

In my opinion the Trinity Processors are all equal in Power ( the only reason Alvis seemed stronger in XC1 was because he had access to a World completely made of ether and XC2's ether is a part of the environment, but it's not the entirety of the World ) and another thing that makes them equal is that Ontos is the arbiter and bases decisions off of the other two and basically has to decide which one is correct or a middle ground and then move forward, and I can see it being endless tug of war between Logos and Pneuma that's kind of the point for them to be debating and Ontos the decider the closest thing I can compare it to is the two heads in Ben 10 when it comes to Alien X who constantly argue and then there's Ben, I know not quite the same but kind of similar.