For me, no. My favorite movie is the Matrix Reloaded but I am well aware it's not the greatest movie. I think it has a lot of really cool things with its writing and direction but it's far from the greatest.
Honestly, most movies I'd tag as "greatest" would be for cinematic reasons and likely won't be my favorite just because it's too artsy and requires brain cells to appreciate.
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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.
Take your pick off the IMDB top 100 honestly. Things like Shawshank redemption, Pulp Fiction, or Forrest Gump. Overall, good movies that really are beautiful but they bore me.
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