"Are you happy?"
I think 高兴 is relatively instantaneous and 快乐 refers to a lasting state. They are often not interchangeable.
When I heard the good news, I felt (very) happy.
I am happy for you that such a good university admitted you.
Happy New Year!
The prince and the princess lived happily ever after.
When translating, usually both are translated to happy. However, as a native speaker, I personally feel that 高兴 is referring to an emotion that is a bit more elated (happier) than happy, but not yet reaching excited. So it is the happier form of happy to me.