Bedtime Story (1964)?
Finally, there is a remake that excels the original in general view; critics and professionals agree and the audience enjoyed the remake. This movie is often mentioned as the exception of the rule that the originals are better. What is even more interesting, when I watched the original after seeing the remake, I recognized many moments almost identical in both films. Yet, the remake is much better, so it goes to prove that Frank Oz is more than just a skillful director, able to produce a masterpiece without altering the original too much. Although Brando and Niven are not bad at all, Caine and Martin are excellent in their roles; I would even dare to say that this one is one of the best Michael Caine's performances in his entire carrier: http://www.movie-remakes.com/film_detail.asp?id=8
Movie remakes compared to original
http://www.movie-remakes.com