I was too young for Ed Sullivan, and i don't recall Dean Martin having a show (probably before my time!).
I did enjoy the Smothers Brothers though. I was never a real fan of Carol Burnett, not sure why. I think I mostly enjoyed the shows which had a musical component.
I think it was the combination of music and comedy along with the odd variety act that did it for me.
I wish they would bring Wayne Brady to network television with this sytle of show. He's be great at hosting a variety show.