There are two main differences:
-Tolkien is high fantasy at its highest. BM actually tries to be low fantasy, despite some magical elements (e.g. daimons).
-The characters in BM are noblemen, which also happens to be the characters in most of Shakespeare's plays. Conan is also low fantasy, but a noble character based on Conan would be out of place in BM (as an adventurer, maybe). Macbeth, however, is perfect.
King Lear, Henry VI, and Richard III are all perfect examples as well from Shakespeare, in terms of SMA. Personally, I would suggest A Man for All Seasons, by Robert Bolt in 1960; based around Henry VIII's time. Fantastic play and present inspiration for my characters .
