De Niro does his tough guy schtick well, and apparently it sells - he's been very successful in doing it for a long time. The, "Analyze This," and, "Analyze That," films show that he's also conscious enough of his schtick that he's capable of pulling off some self-parody, but I think that's the extent of his play book.
When, "Raging Bull," came out way back in '80, the glitterati were all abuzz about how much weight he gained and lost for the Jake LaMotta role and that burnished his reputation as a, "dedicated actor," when the credit would have been more appropriately given to his dietician and personal trainer.
I think the best example of how limited he really is can be seen in 1986's "The Mission." Called to play something other than a 20th Century Italian tough guy from NY, he was way out of his depth and when contrasted on screen with an exceptionally talented actor like Jeremy Irons, De Niro's shortcomings become all the more obvious.
DiNiro is a jerk, but a great actor.
Harry Tuttle is a personal hero.