I like to send in lots of peasents to get slaughtered and all that peasent killing will tire out even the hardiest of elite soldiers. Then when there walls are lined with the bodies of my loyist, and stupidest peasents I send in heavy cavalry to wipe them out. against a tired enemy heavy cavly can somtimes eliminate them with one well placed charge, and the arrow towers are hard pressed to hit a horseman marching at full speed.

For more serious seiges with larger garrisons and castle upgrades you will want to bring units with large shields, shields greatly reduce losses to arrow towers. Although cannons will kill even the mightest of kings, so be wary.