I used to have TONS of Beatle books, but a lot of them got donated or sold along my long and winding road, unfortunately.
Two I wish I'd held onto was "The Beatles Forever" by Nicholas Schaffner and "Growing Up With the Beatles," by Ron Schaumberg. Schaumberg's was unique in that, although it had plenty of Beatle information, it was really the author's "coming of age" story in which the Beatles and their music were always with him, like good friends. His story was interesting and there was enough Beatle information to keep a rabid fan interested.
I actually prefer "Shout" to "Anthology." I still have a copy of "Shout" on my shelf. (I also have two copies of "Anthology" -- two people bought me the same gift for Xmas the year it was published).
As far as books about John go, I liked Coleman's bio and also a book by Anthony Fawcett called "One Day at a Time," which I read at the age of 13. That book swayed me from favoring Paul to favoring John (although I'm probably a rare fan in that I love BOTH of them and can sympathize with both sides of that relationship).
As far as Paul bios go, "Many Years from Now" was great.