I really like "Allied Aircraft Piston Engines of World War II" by White (although it has been over ten years since I read it). I think it gives a good overview of many engines from their creation through development and into service. Of course, I would have liked it to be even more detailed (never too much), and the SAE (publisher) did not use great paper, so photo reproduction could be better. It is really just US an UK engines; there are no Russian or French engines.
"Aircraft Engines of the World" by Wilkinson gives a good snapshot of whatever was going on that year. There is not much history info and obviously types there were somewhat secret are not included. 1945 has known (to Wilkinson) German, Japanese, and a few Russian piston engines, but little on jets. 1946 has jets but nothing on Germany and Japan because the war was over and the engines were no longer in production. In this regard, I liked what the Jane's books did in having German engines that became known post-war. Wilkinson did not do that for piston engines but did for jets.
Really, I feel all these books have their place, but it all depends on what you are looking for (and how much surplus cash you have to spend). As far as I know, there is no book that covers all major engines of all nations. If you want to know all specs on known (and some experimental) WWII engines, Wilkinson can do that. If you want to know more about the major (and some minor) types of US and UK, White has that (much more history).
I keep hoping for a "Part II" of the Allied book covering Russia and France and an "Axis Aircraft Piston Engines of WWII," but I won't hold my breath.