I haven't found one single book that covers everything. Grabau's book is my favorite, but it leaves out the 1862 events and most of the riverfront part of the siege (as do they all). The only way to get everything is through Bearrs' books, even though their quality isn't the best of what's available. To me, Bearrs' sources were the most reliable and most of what others wrote was largely colored by modern-day views, especially Northern (except for Foote's which had Southern bias, but it was poorly written).
I think part of the problem is that some writers consider everything Grant did during the months leading up to the 1863 siege, as being so important that it warranted equal time in their books, and also that different value is placed on the various failed attempts at getting into Vicksburg. A lot of the interpretation of Grant's campaign up to arrival in Louisiana is very subjective - if you don't agree with the writer's interpretation, you'll likely not read the book with much enthusiasm. It's also a matter of personal taste - if it were my choice, there would be a smaller amount of material on everything up to where Grant set up on the Louisiana side, more on the 'probing' that Farragut was responsible for in the summer of 1862, as his interaction with the riverfront batteries had a large impact on the 1863 siege, and more on the river defense during both 1862 and 1863. Most books just focus on the Eastern side of the city and the plight of people in the city, largely repeating the same stuff. Grabau's is the best of such books and from my poor memory, also covers the riverfront part of the siege fairly well, although it has errors regarding battery placement that I found odd.
So I don't think there is a single best book, which is why I have about twenty plus all of the official records.