They both have the same meaning, but 'moving movie' sounds odd, doesn't it? To avoid the repetition, I'd prefer 'the most moving film'. I don't know if a US English speaker would feel the same, but if the two words have the same meaning for you (which they do to British and Australian/NZ English speakers), then it would seem to make sense to choose the phrase which doesn't involve repetition.

It's same

film and movie are the same.Usually "film " is used in the UK and "movie" in the USA but they are both correct and everyone understands them.