There's an important distinction between these courts: while the ICJ deals with disputes between countries, the ICC prosecutes individuals accused of serious international crimes, including genocide, war crimes, and crimes against humanity.
I arrived just in time for a guided tour of the Peace Palace gardens. Something I enjoyed seeing was the collection of gifts and artwork contributed by countries around the world, including an Armenian cross-stone and sculptures displayed throughout the grounds. It was interesting to see how the building's international character extended beyond the institutions housed inside it.
By the end of the day, I was still thinking about my conversation with the walking tour guide. I'd spent much of the trip learning about Dutch history in museums, but some of the most unexpected things I'd learned came from simply asking someone about their own experiences. In particular, I was left wondering how much of what we understand about our countries' histories comes from what we are taught in school, and how much comes from the questions we think to ask afterward.
Unfortunately, cameras and other electronic devices weren't permitted inside the Peace Palace grounds (except in the Visitor's Center), so I could only photograph the building from outside its gates. Perhaps you'll have the chance to visit someday and see the gardens for yourselves!