I don't know about chickens (haven't been at it long enough) but with dogs you couldn't have it both ways. You went for show quality beauty/perfection or you had a dog that did the job he was bred to do...... seldom if ever did you have a dog that could do his job and win in a show ring. So..... do you settle for a beautiful chicken that just looks good or a world beater egg laying chicken. Is that what happens in the chicken world too?
I had 2 out of 3 Rottweilers that were show quality and the handsomest one was not just gorgeous, he was inherently natural at following commands and enjoyed obedience training, was easily socialized with humans, children, or other animals, best working dog we ever had so having it all in one dog breed was not difficult for us.
In our case with Ameraucanas, however, we had sad experiences. We told the breeder we were interested in two blue, not greenish-blue, layers and we were not looking to show. Well, we got two birds where one could easily have been SQ and one was more PQ. The SQ quality juvenile died almost promptly and the PQ bird eventually did lay pale blue eggs (not greenish) - just very very few of them. In her second year she gave 3 eggs only. Only reason she isn't in the freezer is because she has such a sweet non-combative demeanor toward her flockmates - it would be easier to cull her if she were mean but she is so darn amiable. We asked for a balance between blue eggs and a fair amount of them from a PQ bird but we didn't get it. No more show breeders for me - the breeder I got my juveniles from is not even bothering to breed them any more either. This year I ordered a Blue Amer juvenile from a different breeder and 21/2 weeks later the vet had to euthanize her she was shipped sickly. I don't order chicks because they are delicate so I order 2 to 4-mo-old juveniles for better health odds and still lost 2 out of 3 Amer birds.
With 50/50 pro/con feedback from owners about the reliability of blue gene layers i.e. Amer's, EEs, Araucanas, or CLs, I won't be getting any of them. Amer's are the sweetest birds I've ever had but when I'm zoned for only 5 hens and no roos I need every girl to be better than only 3 eggs their 2nd year. The best way to be assured of more blue eggs is to have a good sized flock of birds to make up for the dud layers but when I'm zoned for only 5 birds I couldn't take the chance that half the flock would turn out duds and still have to feed them. One of our friend's EEs didn't lay in her 2nd year either.