I've had both. Multiple times. Purebred, specific dogs and mutley dogs. I've no argument with either. My top three in my life are a very specifically bred English Springer, a Rottweiler (also specifically bred) and Sam, half something and half something else :)
That Springer was a hunting machine-what he was bred for. The best upland bird dog I've ever seen (and I've seen lots) plus he was a just great companion dog. The Rott was enormous and the most gentle creature on earth. Sam just loves everything and everybody (except cats and squirrels).