Byzantine Cavalry is ridiculously good and my favorite cavalry unit as the Byz.

I don't find myself building many Kats. Kats are good, but not great. However, in the SP game, the Byzantines get ridiculously powerful royal generals and their usual +4 valour bonus make Kats great. I find I use Kats to counter charge and a break up a charge of enemy units.

Byzantine Infantry is pretty wimpy moral wise and shouldn't take a full charge. Spearmen suck. Varangian Guard has high defense but cost too much. Kats are heavily armoured and relatively cheap.

I use them as a beat stick in early to counter charge enemy infantry before bashing my BI and VG into them.