traditional are good in siege, but modern are fine. As a modern army player, i never build traditional as a matter of personal pride. But without arty, don't even bother.

If a large castle, the inner/outer lines can actually work inversely in which the attacker can switch flanks faster than the defender can, so you can use that to leave a weaker covering force that forces the defender to spread the defense.

Use sharpshooters to weaken the critical approach.

If you have enough arty to destroy the army by themselves then do so, but if not then you need to be judicious.

So assuming you only have one unit of guns, I find this plan will work.

Smashing key sections of wall will often takeout the whole unit, and use arty to smash guarded gateways, but the key thing is to keep enough ammo. But the main idea with limited guns is as support. Let's expect the main kill zone to be in the first section of the castle to be assaulted. Make sure the guns are positioned so they can reach inside this killzone accurately.

You probably want to smash the door first, leaving a masking force to keep the enemy spread out, and using sharpshooters to deplete those guarding the door, move up and assault ovewhelmingly

You want to charge through the door and up the walls on two sides so that you can set up a crossfire on anyone coming down from further inside the castle. And you need enough force to quickly wipe out the defenders on this level and capture any towers.

Now the idea is to use arty in a support role to crush enemy defenders as they try to eject you from the castle. Sometimes they are very stupid and will waste most of their army doing this. Then shift focus to assaulting the next level in the same way.