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It's hard to say which is better, as I like elements of both. Some say that DiCaprio went too far over the top, in The Departed, but I felt that his acting was better than Tony Leung's. Tony acted like so calm and cool throughout it, that I didn't feel the same sense of drama with him, and what he was going through compared to DiCaprio's portrayal.
I prefer the Internal Affairs ending over The Departed ending. But I prefer how they made the two female characters into one character for The Departed. I also like Nicholson's performance better than the original actor (I can't remember his name).
One of the biggest detractors of the original is that it suffers from cheesy dialogue compared to Scorsese's. I don't know Cantonese, so I am only going by what the subtitles were giving me, but the dialogue just seemed really cheesy or bad at times in comparison.
Like for example,
SPOILER
In The Departed there is the scene where after Quinan is killed, that Costigan and all the other goons are hiding out in the hideout, and Delahunt, says to Costigan "I gave you the wrong address, but you went to the right one", and then Costigan grabs his gun, worried he is going to now have to shoot his way out if Delahunt yells out that he is the rat. But Delahunt is too weak to yell and dies right then.
That was a moment of true suspense.
But in the original this moment doesn't happen, and all the Delahunt character says is "That masseuse you go to... She better not look like a pig, otherwise it's not worth it". And then he dies.
I'm thinking what, that's the best the writers' got? Huh? Even though Infernal Affairs is the original, I feel the remake improves, on a lot of little things, like that, just adding more and more suspense, in comparison.