Cavalry & Cataphract Striping
It's actually not that hard to strip cavalry and cataphracts from a city once you get used to it, however you need to know when you need to do it and when its not a good idea. I'll go over that after I go over how to strip the ponies out of the city. There are two scenarios where the tactics you use to remove the cavalry and cataphracts are different.
Scenario 1 – Traps, Trebuchets & Abatis
The first scenario is if the defending city has ANY traps, trebuchets or abatis. If the defending city does have them this will set the starting range at 5000. Thus the defending cavalry and cataphracts are going to rush up and smash into your army long before the rest of the defending army arrives.
You have a few options at this point, you can send a tone of warriors at him or a layers + archer attack. If the target city has quite a few traps, trebuchets, and/or rolling logs I would highly suggest you use warriors. Nail two birds with one stone, take out his wall defenses and his horses at the same time. However if he doesn't have many traps, trebuchets, and/or rolling logs I might suggest the archer/layer attack. It can be more efficient and is considerably more efficient at taking out cataphracts. Your layers have to be thick enough to last a few rounds vs the wall defenses (ie no 1 unit layers) but making them too thick will make your attack less efficient. Estimating what those numbers are is based on intuition largely at this point but I have some general suggestions for the makeup of your attacks:
General Suggestion Warrior Attack:
Warriors = 6 x cavalry + 15 x cataphracts
General Suggestion Archer Attack:
Layer Thickness = 25% x (traps + logs + trebuchets)
Archer Count = 1.5 x cavalry count + 3 x cataphract count
use warrior(1) + pikeman + swordsman layers + workers(1)(2)
(1) these units can be left behind if you need speed, but will make your attack less efficient you may need more archers.
(2) workers will also work as a layer in addition to warriors, pikemen & swordsmen layers but not without them.
Now don't forget, these attacks are designed to lose thus you might lose your hero. Don't use attack heroes you can't afford to lose on these attacks. However don't use horrible heroes also. You do need to put out a lot of damage. Also you can use just mass pikemen, instead of warriors they can be very effective, however you will always get more bang for your buck if you use archer/layer attacks in scenario 1.
Scenario 2 – No Traps, Trebuchets, or Abatis
This is generally a stronger defense making our jobs considerably tougher. Archers become useless offense in this situation. Your archers will always target enemy Archer Towers. With crazy health and the best defense in the game you might as well be hitting a brick wall with arrows. (read the best defenses guide for more info on this).
Here's what you need to do. You need to send a few of every unit up to cataphracts and either a tone of warriors or a tone of pikemen. Warriors become extremely ineffective against cataphracts in this situation. Pikemen are considerably better but obviously less effective than we'd like them to be. And like I mentioned before archer/layer becomes a useless attack. The more rolling logs your target has the thicker your layers need to be so they don't die to the rolling logs.
Suggested Attack with Warriors:
1-100 units of each of these: swordsman, pikeman, archer, cavalry, cataphract
warriors = 10 x cavalry + 22 x cataphracts
Suggested Attack with Pikemen:
1-100 units of each of these: swordsman, archer, cavalry, cataphract
pikemen = 2x cavalry + 5x cataphracts
Again these suggestions can be highly influenced by intuition. There are many factors not taken into account here including enemy hero attack and the hero attack that you have on offense. However, while I might edit how many I attack with I don't remove entire types of units in my attack.
When to Layer Strip Cavalry & Cataphracts
Before you get all excited on trying this out you have to realize there is a situation where you do NOT want to strip cavalry and cataphracts from a city. That situation is when you're planing on attacking a city that has any abatis, traps or trebuchets, with an archer spearhead and the defending city only has a small number of cavalry and cataphracts.
Why is this? Well when you attack the city his cavalry and cataphracts will race forward ahead of his army and come in range of your army with no backup, your army will stop moving forward for a round or two to kill off the cavalry and cataphracts (at little to no cost to your army). This means it's considerably less likely that you will engage the enemy while in range of the enemy archer towers. Thus letting you pick off his army in stages instead of trying to take it all down at once.
There you have it in a nut shell. How to strip Cavalry and Cataphracts from defending cities.