I've barely scratched the surface of Bangkok and have seen even less
of Hong Kong, but I agree with your concern that Hong Kong, while
quite different from the US, is far more westernized than Bangkok.
Given that you have 11 hours in Bangkok, and there's no rush hour on
Sunday (I know, it's always rush hour in Bangkok), you'll probably end
up with at least 6 hours in town. That's enough for the Royal Palace,
a great meal, and a couple of hours wandering around.

You would certainly have a fine time in Hong Kong as well. I'm sure
there are plenty of non-westernized places there that I just don't
know about. But as long as you don't mind the chaos of Bangkok, I
think it'll be more interesting, and it's definitely doable.

Do check the hours -- according to my (old) guidebook, the palace is
open on Sundays but closed (daily) from 11:30am-1pm.

Bruce