Hello pgabl1! I hope it's not too late to respond to your question. We just returned from the Golden Princess (2/7-2/14).
My husband and I love the "anytime dining" option. We like to eat according to our own schedule. The menus and the quality of food are the same for "anytime" and "traditional." The only difference, I think, is that some people like having the same waiters every night. That's not an issue for us. Also, I heard that "traditional" diners see a Baked Alaska parade one night. Again, that's not an issue for us.
I hope you have a great time on the cruise!