You know, some times there is little point in asking these things, because even the writers aren't too sure themselves. Even know, it looks like they are trying to tidy things up from the Yoshida Meteor.
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I personally think the difference is rooted in the mindset of those involved in the summoning.
Much like how the Ifrit the Amal'jaa summon is based on their conception of Ifrit, the difference in the physiology of Primal Bahamut could have been a result of Tiamat's emotional and mental state at the time.
The result - a larger deiform (assuming it was summoned at it's size we saw during the Calamity) with strong legs, a broad chest, and a singular but powerful set of wings in contrast to the multi-part wings of the original's kin. Something more war-like, possibly as a result of a desire for vengeance from Tiamat, goaded on by the Ascians involved?
If you don't mind me asking, is it confirmed that the first brood all had the same body-type?
Considering Middy has shown himself in 3 forms ranging in size and wildly different shapes (dragon pup form verses miles long serpent) and the different dragon sizes and shapes from the individual broods, I wonder if Bahamut was just genetically predisposed to have different appearance, or if a dragon's appearance directly correlates to their current level of aether/power.
During the Final Steps of Faith, Nidhogg assumes a pose very similar to Bahamut while the shadow dragons are attacking. By comparing Bahamut Prime with Nidhogg, I noticed that Bahamut's body actually has a morphology similar to his siblings, but more robust and with distorted proportions (enlarged torso, elongated wings, relatively small head and forelimbs).