Fundamentally, they are not the same question, as the greatest movie implies an objective comparison of some sort, whereas favorite movie implies a subjective comparison. Quite simply, the movies that we could watch over and over tend not to be the grandest undertakings.
For example of one reason, the movie 告白 (“Confessions” is the English release title) is widely regarded as an excellent example of Japanese “shocking” genre; I could spend hours lauding its virtues, but after tearing the movie to pieces in my analysis for Japanese Film class, it is no longer shocking and I don’t desire to watch it again.