I've not tried keeping CPQs. I chose coturnix mainly because, like my hens, they are dual purpose pets which are a lot of fun but also lay very large numbers of edible-sized eggs. Also, the nearest breeder to me only bred coturnix.
I don't think one is better than the other, just different. I expect many people interested in quail try them both in the end. It's been interesting for me to read posts from you CPQ people, to find out what I'm missing!