I agree that the Inchoroi in the Warrior-Prophet epilogue is Aurax. Aurang is still bound to a Synthese in that time and I got the impression that isn't something you can just turn off and flit back into your own body in an instant.
As to him not showing much of a distinct personality...well, we saw very little of him. And what we saw of him involved him doing things are basal to the entire Inchoroi species. They recognize this themselves. "We are the Race of Flesh. We are the Race of Lovers." To the Inchoroi, everything is about sex. They're like if geese or bonobos or similarly over-sexed animals became sentient and developed a culture.
We can glean some of his personality from his other actions though. Aurang, not Aurax, is made the No-God's horde general. We can therefore assume that he possesses qualities desirous in a general that Aurax lacks. He is probably more decisive, more bold. A man of action, as it were. His personal presence (although within the synthese) in the Three-Seas managing their spies (a very dangerous task mind you, one lucky hit with a Chorae and he's a bird-sized pile of salt) confirms this.
Aurax meanwhile very rarely is mentioned in the histories we know or in the series. He is the one cited as giving the (remaining) secrets of the Tekne to the Mangaecca. Since Aurang and Aurax are described as twins, they were by necessity born at the same time. That means they each had just as much opportunity to learn the Tekne. They did not pursue this option equally though.
Aurax is the nerd of the two. He's likely more prone to inspiration and intuition and introspection and curiosity, less prone to action. He deals in grand plans and theorems, not actions or the minutae of tactics and logistics.
Aurang is a soldier. Aurax is a scientist. They're both monstrous alien organisms of immense narcissism and horrific appetites. But their chosen vocations gives a hint as to the things that separate them from each other.
Here's looking forward to seeing more of both the twins in Unholy Consult.