This gets into generalization, but I don't think the overall concept of a seige would vary much because of how a castle was designed. Specific tactics might vary a lot based on specific layouts, but the overall concepts are pretty much the same.

Castles work (or "worked) because it is difficult to take them from a defending army. The concept of a seige is not about storming the castle, although that somtimes did happen. It was about surrounding the castle, and keeping the people inside from going out to get food/water etc. As seige equipment became more advanced it became possible to break down city and castle walls and sieges became about breaking the will of the defenders before breaking the walls.

For example, The seige of Ishiyama Hongan-ji - It's wiki, but backed up by cites to Sansom, George (1961). A History of Japan: 1334-1615. Stanford: Stanford University Press, and Turnbull, Stephen (2003). Japanese Warrior Monks AD 949-1603. Oxford: Osprey Publishing.

This occured during Oda Nobunaga's attempt to unify japan. The Ishima Fortress lies on the coast of Japan, and a naval attack was impossible because Nobunaga did not have a dominant navy. 15,000 men were defending the fortress compared to Nobunaga's 30,000.

Several attempts at direct attacks on the fortress were repulsed. Nobunaga then settled in for the long haul, and from 1576 to 1580 he blockaded the fortress, defending himself against sally attempts by the Ikki. The Ikki then surrendered in April 1580 after a direct request by the emperor (at Nobunaga's request).

I think the other comments pretty much covers the attacking of a Japanese Castle.

Although this could be kind of irrelevant, I though you might be interested in the defense tactics of some of these castles too. (I learned a lot while I visited some of the castles in Japan).

Apart of the obvious moats and the walls, these are what I learned:

One thing I noticed first was the maze-like structure that leads to the center of the castle. Himeji Castle, the one I found most amazing, has very complex maze systems that is very hard to follow.

Another defense aspect of these castles are the extremely low gates and narrow roads that lead to the central tower of the castle. There are many small gates all over the maze that doesn't allow horses to pass. The narrow roads limit the number of foot soldiers that could come it at once.

Another interesting thing are the vegetations that grow along the side of the walls. These plants (I forgot what they were called :/) are very slippery and hard to grab. The plasticy texture on these plants prevents soldiers from climbing the walls.

Another interesting things are the structures of the road that leads to the central tower. The roads in Himeji Castle are made up of downhill roads that lead up hill. So basically, the attacking soldiers would try to go uphill in order to reach the central tower. But because the roads that lead up hill are slanted to look like they go down hill, attacking soldiers get confused.

When I was touring Himeji Castle, I came across a oddly protruding room that was positioned on a huge log on top of a hill. Basically, when the attacking soldiers came across, they would push the log out of position, which causes the protruding room to fall on top of the road. The room served as a weapon to crush the soldiers, and to create a blockade.

Thinking of such defense tactics, attackers would have had a very hard time if they simply charged into these castles. Because of this siege tactics would have been preferred by the attacking side.

This answer to a similar past question may be helpful.