Ambrose wrote books for the general masses, not for higher understanding of the material. He was known for plagiarizing material, too.
Band of Brothers has its place, though.
Omaha: A Flawed Victory. Overlord (there are two by that title, you want the one by Max Hastings). Decision in Normandy. These will give larger views of the total battle.
Also depends on what you want to focus on. Individual units? Bedford Boys is good.