In both movies there are several depictions of the character of James Bulger who added each other, blurring the profiles by reading related texts and through the testimony of repentant former members of the criminal gang that Bulger was the head, probably outlines the complete profile of the person in question.
Bulger of Nicholson, represented precisely in the movie "The Departed", is a homicidal maniac with a grotesque note; Bulger of Depp, depicted in the movie "Black Mass" is a pissed off homicidal maniac with a bipolar note.
In conclusion, then we can assume that from what the texts says and the repentant said, the real Bulger is probably a mix of both.
Bye