Di Caprio is boyish-looking, and quite fair. Rasputin looks very dark in all his photographs, with long hair and a shaggy beard, and looked his age (mid to late 40s at the time of his death).
I have no idea what J Edgar Hoover actually looked like, so it would not be too much of a problem to have Di Caprio play him. But Rasputin is a very recognisable figure, so if I were making a picture about him, I would start with someone who was a reasonable likeness to begin with. Tom Baker was very good in 'Nicholas & Alexandra'.
Ann