Peter, those two books were written by different authors.
The novel Fail Safe , was written by two political science professors, Eugene Burdick and Harvey Wheeler. (I have never read it)
Dr. Strangelove was based on the paperback novel Red Alert (1958) by Peter George. George collaborated on the screenplay with Kubrick and satirist Terry Southern. They also published a novel after the movie, which I read, that is quite fun, but after seeing the movie, doesn't add much more to the cinematic story.
You give an interesting parallel. I have more fun with DR. Strangelove than I do Fail Safe as Dr.S has much more to offer for multiple viewings. Once the suspense is over in FAil Safe, well, then it isn't so much fun to watch again. Perhaps this correlates to whether I would play Winged Foot or North Berwick. I suppose for competitive thrills of suspense, Winged Foot might do it, but, since I'm not competitive, in a human or skillful way, nor do I have access to WF, I'd have to say North Berwick gets "put in the DVD player" again.
BTW, I've never heard a discouraging word of Lumet's body of work. A true craftsman of cinema.