One of the fundamental differences between the Third Imperium and the Zhodani Consulate boils down to ...
Hereditary Aristocracy vs Individual Meritocracy ... if you can believe that.
Think about it.
In the Third Imperium, what is required to become an imperial noble at the top of society?
Short Answer: Social Standing.
Slightly Longer Answer:
Hereditary Social Standing ... meaning that you need to
"choose your parents wisely" (or words to that effect), in order to be "born on third base" before scoring a home run (essentially).
Every member world of the Third Imperium needs a Knight (in post) to represent that world in subsector/sector/domain/imperial politics, but as you advance up the Social Standing ladder, there are fewer and fewer postings at the rank of Baron, Count, etc. all the way up to Duke ... so as your Social Standing rises, the "club" gets more and more exclusive simply because there are fewer and fewer positions to go around, yielding an essentially feudal hierarchy that calcifies over time into a hereditary aristocracy (your children are born at -1 Social Standing to their parent(s)). So while there is SOME social mobility possible through individual merits and achievements, truly "joining the club of aristocracy" is the work of generations, not necessarily of individuals.
So although there is a limited amount of "churn" in the ranks of the imperial nobility, there is enough "friction" involved to put a lot of emphasis and advantage on incumbency ... which then results in family dynasties of aristocratic privilege that are able to perpetuate their wealth and power relatively easily, compared to an "upstart challenger" who has raised their Social Standing through their own actions during their own lifetime. Remember, being posted somewhere as an imperial NOBLE is a Career Choice(!) ... not just a matter of merely buffing your Social Standing stat (which makes you an "honorary noble" rather than one posted to a position of responsibility representing the Emperor to specific worlds as a vassal to the Third Imperium). This then helps with stability by preventing too much turnover (churn) within a single generation and protects the incumbency of particular families and dynasties that can accumulate wealth and power unto themselves (and all the corruption of purpose that implies).
Compare that to the Zhodani Consulate. What is required to become an Intendant at the top of society?
Short Answer: Psionic Power.
Slightly Longer Answer: Because psionic power is NOT hereditary(!) ... the most privileged in society CAN BE ANYONE FROM ANY FAMILY ... they just need to be psionically gifted and powerful.
This means that the "upper crust" of Zhodani society has a TREMENDOUS amount of "churn" in the ranks, effectively preventing the sort of dynastic hereditary strategy of accumulating wealth and power with each succeeding generation that is so common as to be expected (and widely accepted!) in Imperial society. Social privileges are conferred upon the "worthy" (measured individually) rather than upon the "hereditary" (who were your parents?). It's a meritocratic rather than a dynastic system, which privileges the importance of psionic power and skills.
"A sound soul dwells within a sound mind and a sound body."
Can you see how foundational and fundamentally at odds such concepts of societal organization are?
There IS NO WAY to reconcile the underlying structures of these radically different ideals of hierarchy and merit.
Of course the two cultures would clash and be at odds with each other ... even before adding in the wildcard of competitive advantage that psionics training brings to the table, such that a (so called) "level playing field" between the two parties isn't even meaningfully an option in high level negotiations.
THIS.
And thus the pattern was set for centuries of hostilities over successive generations, due to irreconcilable differences of ideas about individual merit vs heredity privilege.