Again, depends on what is meant by 'best'. Out of those four, I'd go for Liddell Hart's single-volume history as 'best' as he had personal access to many key figures from both sides. Keegan's is probably 'best' written and has a more modern perspective, but he only analyzes a few key areas in his book. Churchill's is 'best' as in most historic and an insight into his thinking, but doesn't work overall due to his personal bias and obsession with his own place in history. Ambrose I'm afraid I wouldn't place in the same category as the other three.....
Again, if you mean 'best overall history of WWII in one volume', I'd probably go for the Liddell Hart, but it doesn't include much post-war research and revelations - ULTRA, for instance. Calvocoressi/Wint's 'Total War' is also quite well-rated but skips over some important areas, and isn't as readable as Hart's. And then, Martin Gilbert's book is OK and benefits from modern research..... But really, WWII is such an enormous and complex subject that any short history is going to be a huge compromise and can only serve as an introductory text. There is a 'best book' for just about every campaign and even many individual actions in the war, many of which you'll find discussed further down in this topic heading ( ie 'Best D-Day book', 'Best Bulge book', 'Best Bomber Command book', 'Best Arnhem book' , etc...)
Not only that but it really would depend on which theater you are looking at. From what I remember (correct me if I'm wrong) but even Liddell Hart's overview seemed to gloss over the Pacific and CBI Theaters. I would have to say the Morison's single volume work "The Two Ocean Navy" or Toland's two volume "The Rising Sun" probably give the best overviews in terms of the Pacific Theater but even these gloss over the CBI theater. Frankly in my opinion there is just too much that happened during WWII for any one volume book to fairly try and even give an overview of all of the theaters. Your best bets would be to check any of the three that Martin listed for the European Theater, either of the ones I have listed for the Pacific should your interest lie there. Unfortunately I don't have too much information regarding CBI theater but I have a feeling that either Ali or TA might be able to help you in that regard.
These are my personal choices - others will offer different suggestions : For me, the best overall book about D-Day and the Normandy Campaign is Carlo d'Este's 'Decision In Normandy'. For a popular history of just D-Day itself, I'd probably still go for 'The Longest Day' by Cornelius Ryan. From the German POV, 'Invasion - They're Coming !' by 'Paul Carell' is a great read, but biased ( the author was in the SS....) Sorry, but I just can't bring myself to recommend Stephen Ambrose
I wouldnt say its the best book, but i loved the book The Longest Winter. A very good story of the battle of the bulge, with many stories of that company after the war as well
