We also went to the old St Paul's, which was a beautiful building. Early plans had been to demolish it, but it was saved. It is one of the nicest old wooden buildings I've ever seen. Interestingly the two flags on the right are a US Marines flag and the US flag. It remains consecrated but has no congregation and is only used for special events such as weddings.
The Capitol is an interesting mishmash of architecture. The building on the left is called the beehive and is used for offices although there are lots of complaints about the difficulties of using a round building. The middle building is where the Parliament meets and looks like such a building. The one on the right which I thought might be a church at first but since there was no separation-between-church-and-state in this case clearly wasn't - it is a library. There are many other examples of modern architecture juxtaposed more conventional buildings or wooden sculptures.