Hcats backed by HAs are quite a powerfull force, especialy when Hittite, or sumarian.
Against this, I like to use Scythes due to their inexpensive nature. Scythes are better than camels due to their increased hps, no gold cost, and trample damage which makes up for damage modifier camels have.
Mass rushing scythes with out proper planning will still get you killed. The problem though is that even with reduced balistics, his cats will be hitting your scythes behind the one in front, so by the time they reach your opponents forces, their will be so few left the HAs will chew em up.
Stagger your units as they rush, or try to line them up horizontaly before you attack, so his cats wont be hitting you.
Like sandyman said, attack his HAs before his cats, why? because the chances are his Cats will fire at your Scythes as they engage the HA, which will cause his HA to be the victims of friendly fire.
Egyptians are naturaly the best for this with their Scythes, that can take a beating. They also got those 16 range priests, which are great to convert a cat, and have it fire upon the HAs massed Legions (choson) and AE (Persian, and Carth especialy) are other ways of dealing with cat, HA combos
Of course....you could go Hittite your self, and just out cat him