This was the slogan of Lucky Strike cigarettes; the TV commercial showed a man with a black eye saying "I'd rather fight than switch." This was, of course, before cigarette ads were banned from TV. All kinds of tobacco products used to be on TV, like the Marlboro Man; he was a very macho-looking cowboy who smoked only Marlboros, of course. The Camel cigarette ads said "I'd walk a mile for a Camel." The implications of these ads was that to be a real man, you had to smoke these cigarettes. If you know the words to the Rolling Stones' song, "Satisfaction," one of the lines is "he can't be a man cause he doesn't smoke the same cigarettes as me." These were really popular and powerful ads, aimed at men. There were also ads aimed at women, mostly for Eve cigarettes that were long, slim and elegant. Urban legend has it that the actor who portrayed the Marlboro Man died of lung cancer from smoking.
As I recall, Lucky Strike used the phrase, "Lucky Strike Means Fine Tobacco." Yet, I admit, when a radio host (just now) said he thought it was Tareyton cigarettes that used the phrase ...Rather Fight Than Switch," I also immediately thought of Lucky Strike. It's interesting that more than one of us thought of Lucky Strike.