When did the debate over the stile antico and the stile moderno take place?

During the transition from renaissance to baroque in the 17th century and into the early 18th century.

"Stile antico" was a composition style that paid attention to previous historical trends, whereas "stile moderno" encouraged more freedom and variation in style. Johann Sebastian Bach would be an example of a composer working in "stile antico," deemed more appropriate for church music.