By far the most interesting part was the decisions that we got to make in the Throne Room. It always made me feel more invested in the Kingdom when we had to decide, for example, if we should hire spellcasters or swordlords as military officers, if Necromancy should be allowed or how to deal with slums.
It seemed like the kind of thing that would allow for more flavor and make the characters feel like they're truly calling the shots in the country.