In my English Campaign I always kept at least 1-2 units of Holibars in every stack specifically to ride down any fleeing generals or knights -- I definitely noticed in several battles that armored cav (all types) couldn't catch up and chase down fleeing calvary very well at all compared to Holibars. Most of the time I'd send mailed knights after a fleeing general, the general would get away. But the light cav would almost always get him, even if they had to close a bit of distance first.

Similar thing in my Turks campaign, I always try to have a pair of Turkomans in the stack for the same purpose.