I second that it should be the Cataphracts by far. Chariots usually do not hold up in archery duels. Once their hit points are worn down, they fall very quickly. You just have to last that long. Just put your Catas in open formation when you shoot it out. That will make your people harder to hit and not tire them out.

And yes, skirmisher units receive a +6 bonus vs. Chariots. Mercenary Peltasts are great here.