I believe that each type of protein meat in a raw diet for cats and dogs has its own unique role. I think red meat is the most biologically appropriate food for dogs, so I like to use it as the core protein meat of their diets. Then I'll add some chicken to balance the meal so it won't be too rich.
Cats however are more fish and foul eaters, so using chicken as a core protein is perfectly fine.
One thing you should take note of though, is that most of the chicken products include skin and crushed bone. Consequently it's loaded with calcium and a lot fattier than the lean skinless chicken you see on nutritional charts. Many people go heavy on the chicken when their pet needs to gain weight, so if you're pet is a little on the heavy side, go easy.
Chicken is also absolutely the best meat to use when you are transitioning your cat or dog from kibble to a raw diet. It's bland and easy to digest. Another benefit of chicken (with crushed bone) is that it's an effective way to combat loose and runny stools. When my dog has an upset stomach, I immediately grab for the chicken. And it never fails: his tummy stabilizes in no time. Ditto for cats.
I think of chicken as the ultimate raw-diet sidekick: trusty, reliable, a meat you can count on when the going gets rough, but gentle enough to blend into any meal. Like my late Great Aunt Ida used to say, "Add a little chicken to your life."