Siege weapons are often overlooked, but if you have an enemy you want to punish and can't seem to kill enough of their troops or steal enough resources, you can always downgrade their cities. Even their main can be downgraded, but for each city you must have enough weapons to get the job done.
Siege Rams are used to downgrade the level of your opponents walls, while mangonels will destroy their towers. To make this work, it is recommended that you send +5 more of either than the level of the object you are trying to destroy. For instance, if the enemy has level 12 walls, you want to send 17 siege rams. In addition to this, you must have that +5 ratio in order to reach beyond the walls and attack the structures inside the building. Otherwise, only the walls and towers will be affected. No structure can be completely destroyed and will not drop below level 1.
Each attack must be sent as "Invade" rather than "Raid" and will only downgrade 1 structure per attack by 1 level. The number of troops sent is not important, so long as there are none in the city or enough to kill what is already there. If any form of battle takes place, there is a chance of losing siege weapons, just like troops. The weapons do not have an attack nor defense rating and will be destroyed randomly based on the outcome of the battle.
Some buildings cannot be harmed. Those include: Farm, Quarry, Sawmill, Iron Mine, Shelter, Storage, Warehouse, Granary, Espionage Center, Infantry Barrack, Cavalry Barrack and City Hall. It seems like all the good buildings are gone, but this is not so. The real prizes to destroy are the Command Post, Stable, and Forge. Without these buildings, troop production will slow down dramatically and only 1 military order can issued. This means that if you reduce these buildings to level 1, your enemy will become too weak to fight back, thus giving you the complete upper hand.
At low levels (1-5) you can use +5 more catapults than towers and rams than walls
At mid levels (15-20) you want to use +10 more of each
At high levels (26-30) you need +15 more of each. At L30, you need 45 of each.