In addition to Frankenstein's Creature, the Mummy and Dr Fu Manchu, Boris Karloff and Christopher Lee have also both played Rasputin: Karloff in 1953's The Black Prophet from the series Suspense; Lee in Rasputin: The Mad Monk (1968).
The trivia item below may give away important plot points.
The censors successfully lobbied to have three scenes omitted: (1) The close-up of the leg amputation. (2) Christopher Lee's stabbing the night watchman in the back. (3) Boris Karloff's throwing acid in Lee's face.