I fail to see where the two are incompatible. "Easterners" knew and used the couched lance technique too (the Arabs called it "Syrian attack" around the Crusades"), just not as on as massed scale or as much specialization as the "Franks" were wont to.

Although for that matter, the Franks in Outremer learned rather more tactical control than was the norm in Europe right fast - they kind of had to, the maneuver-crazy locals would've eaten them alive otherwise. Sort of like you don't have to hang out at the edge of the steppe too long to learn the wisdom of a fairly cautious approach to combat.

Anyway, if cataphracts for some reason that quite eludes my understanding did not or could not charge, one cannot but wonder what the heck would have been the point in raising such expensive troops at all ? Armoured cavalry was almost without expection designed for shock assault duties, to ride with near impunity through storms of incoming fire that would decimate lighter troops and smash the enemy apart in close quarters. If you could use them for something else (many, and among some nations apparently about all, "eastern" cataphracts and clibanarii carried the same composite bows as other cavalry), swell, but shock action was their designated specialty field.

Charge discipline is a question of troop training and drill, not of the exact weaponry and technique used. And by what I know of it the Byzantines (and their troublesome neighbours) tended to drill their cavalry pretty well, much better than was even dreamt of among the feudal jigsaw-puzzle hosts of Europe. The open spaces of the East were the natural terrain for mobile cavalry warfare, and to be genuinely good at that you really needed to know more than a linear charge.