As your enemy's walls become stronger, archers become more useless in the attacking army. What you need is infantry, as heavy as you can get it, stocked with siege engines and banners. The more siege engines you have, the easier they will manage to get onto the ramparts. Once you're on them, the quality of your troops' equipment and their training and cohesion can be the difference between victory and defeat.
People tend to think that it comes down to raw CS, but in a siege battle I would much rather fight with a 40 man unit at 600 CS than an 80 man unit of the same strength. Some people still believe that as long as your enemy doesn't have at least 2:1 odds in CS, they will not be able to win a siege of a fortress (level 5 wall), which is a bunch of crock. About a month ago, Darka, Eston and BoM besieged a city of Coria which had a level 5 wall. The total CS values were 19,000 for the attackers vs 11,000 CS for the defenders. A lot of people would think that Coria should have won a close victory, but when the battle was over the attackers had won, with over 14,000 CS still standing (excluding wounded troops that healed later on), whereas the defenders were almost completely wiped out. The reasons: The attackers had about 4 times as much infantry as the defenders, of much better quality. The attacking infantry was well-trained, well-equipped and well-organized, whereas the defenders were mostly mediocre, poorly trained, unorganized militia.
Taking a lot of banners with you will also help a great deal, as your men will keep their morale high, and as a result they will be able to put in a bit of extra 'oomph', as they say. They will be able to take a lot more punishment before being forced off the walls or off the battlefield. In the siege I mentioned, the attackers had a whopping 20 siege engines and 51 banners in the first round of battle on the walls. As a result of this, and the superior quality of their troops, not a single unit of attackers was repelled from the walls in the first round, which proved to be crucial. The defenders managed to hold their ground for another turn, but after that, it was more a slaughter than a battle.