Ok, you´re correct. So I correct my question:
A 50 Khuzait army against a 50 Empire/Battania/Sturgia/Aserai army, which army will have 3/1 cav units?
The Khuzait parties have about 40-50% cavalry early in a campaign but that drops off one they start recruiting from other places, down to around 30-40% once they eat NE/Sturgia.
edit: To be clear, that is still a lot of cavalry but the early-game advantage doesn't work late-game because Khuzaits are majority non-Khuzait lords (usually Imperial), with majority non-Khuzait troops. It's just snowballing more fiefs, more recruits, more parties.
How much bonus do you want to give the Cataphracts so they stand a chance when they have 2-3 Cathaphracts / and 3-5 lower cav units in a 50 troop Empire army? While facing this 40+ cav Khuzait army.
None. If you're a force of fifty with 5-8 cavalry, facing down a force that is equal in size but with 35-39 cavalry, you're in for a rough time.
My preferred solution would be giving rural notables in villages bound to the central Midlands' towns an automatic +1 daily influence bonus when under Imperial control, so they'd much more readily produce noble troops. From there, Imperial armies -- at least those recruiting from their core lands -- would naturally recruit and train more cataphracts over time. It would make control of interior Empire land meaningful for a reason beyond "it exists, therefore I must take it."