Recently, reading a critique of a contemporary French director, I was rather amused to see the author of that book state that, in the 50s and 60s, Positif was a less vociferous but more politicized rival of Cahiers du Cinema. It is my speculation that that author has not devoted a great deal of time in the archives researching either magazine. I would also have to say that pulling off being less vociferous while being more politicized is one neat little stunt.
He also reminded me of this little tidbit from Yale French Studies No.17 1956, an issue dedicated to Art of the Cinema. On page 110, in an article entitled Books in French on the Cinema in discussing French film reviews, it is stated:
"Cahiers du Cinéma (monthly, founded in 1951, deals with film as an art form; lively and controversial; scenarios general news)
Positif (a younger rival; contributors sometimes dogmatic, and violent in tone)"
That issue is available on-line at the JSTOR site for either subscribers to that services or card-holders at libraries which subscribed to that service.