Well, the first thing I want to say is I that I’ve seen „Infernal Affairs” before this movie, so I will draw comparisons.
American remakes of international cinema hits are often a disaster, so I have to credit to Scorsese. The cast is very strong (Leonardo DiCaprio, Matt Damon, Jack Nicholson, Martin Sheen, Alec Baldwin,..), the acting is definitely one of the movies strong points.
The story is more or less the same as in „Infernal Affairs”. You still have your undercover cop and your undercover gangster and the game of cat-and-mouse. It just takes place in Boston instead of Hong Kong.
My biggest issue with “The Departed” is its length. “Infernal Affairs” is a tighter movie, you’ll see the credits after 101 minutes. “The Departed” needs 151 minutes, nearly an hour longer.
What does the additional 50 minutes get you? An irrelevant love triangle (Damon’s GF and DiCaprio’s therapist are two different characters in IA), an inferior ending (the bad must be punished..) and unnecessary new characters (Alec Baldwin e.g.).
In IA Chan (the equivalent to DiCaprio character) is undercover for 3 years, in TD only for one. The whole concept with his therapist is a lot more believable. The two main characters meet very early, without knowing about each other. They’re both present in the same location more often, which helps to get the view more involved.
TD wastes too much time for little things. The gangsters are just evil, they’re brutal and harass women, so everyone understands who the bad guys are. And I don’t remember seeing so much blood in the original movie. IA concentrated on the matter and is not distracted by such things.

You’ve probably guessed by now that I like IA quite a lot more. It’s more compact, the characters are better and the visuals are better.
I gave IA 9/10 and will give TD a 6/10. It’s an enjoyable movie (probably even more if you haven’t seen the original), but if you’re not afraid of Asian cinema, do yourself the favour and what IA instead or at least before TD.
By the way, IA is a trilogy. Infernal Affairs II is a prequel and develops the characters back story even further. The third one is half prequel, half sequel and gives closure to the whole story.