We can look at publicly documented trust fund kids or other (financial) elites and their behavior to get an idea and it runs the spectrum. Princess Diana. Prince Andrew. Paris Hilton, both when she was in the news every day and the quieter stories that have surfaced since. 50 Cent's talked about his child preferring to have money that he didn't have to work for.
It's not the same since they exist in a world where most other people aren't at that level, but we can see that the human psyche isn't always able to manage it.