The debate over which ’60s-spawned band is best has raged for decades, but renowned Chicago rock critics Jim DeRogatis and Greg Kot claim the question has never been the focus of an entire book. Well, now it is. In The Beatles vs. The Rolling Stones—an attractive volume loaded with rare photographs and memorabilia—the hosts of the nationally syndicated public radio program “Sound Opinions” purport to make definitive arguments based on such head-to-head categories as singers, musicians, albums and managers. When all is said and done, though, they determine that (surprise!) both bands have their strengths and weaknesses—leaving readers better served to rediscover those on their own.