Having played that game as the Dragon Knights, here's the flaws I noticed and how I'd fix em:
*If you could somehow make the lances longer, the flying dragon cavaliers could turn out to be totally awesome. Give the riders the ability that Heavies have to carry large weapons, then give em some boneriffic huge blade. Mounted on the dragon and using the size and flight speed of the dragon in a charge attack would allow them to perform some serious
charge attacks. Depending on how intelligent your dragons are, they might be able to throw a flame attack in there too! When I was playing BitS, this is what I was attempting to do, but the reach on the lance couldn't make it and they got killed horribly.
*Definitely keep lances on all the horsemen as well, because that charge attack I tried to make against the bulls (who were supposed to be weakened by the dragon charge but you know how that went) was underwhelming as all hell. But that's just how the dice roll sometimes. I also could have been smarter about when I charged, but ah well.
*Still, mounted archers on the dragons are pretty damn awesome as well. Archers to the rear with spearmen and swordsmen are great as well, but those Pikemen in BitS held their own remarkably well. Putting them on horses is always a welcome upgrade though!
The Dragon Knights fell partially due to bad rolls, bad commanding, and overwhelming forces. I started off sandwiched between the front of the entire bull army, and on the closest front for the Golden Lions. Instead of staying my ground and defending my position, I tried to engage both forces directly with superior units. I disrupted the living shit out of the battlefield, but paid for it with my own life. Then again,