My gut said DiCaprio out of my love for The Aviator, but after taking a second...
Going by performances. De Niro has Taxi Driver, Raging Bull, The King of Comedy and Cape Fear. Although he is excellent in Goodfellas and Casino, I think of those as better movies on the whole as opposed to De Niro giving a strong performance. He's great in them, but in the others there is more a sense of how he carries the movie as opposed to being a cog (even though he is the main character in Casino). His performances in the four I mentioned would garner him top 5 of the year, while he probably wouldn't make the top 10 for Goodfellas/Casino.
DiCaprio has The Aviator, Shutter Island and The Wolf of Wall Street. What I said about De Niro in Goodfellas/Casino kind of applies for how I see DiCaprio in Gangs of New York/The Departed. So that's 4 movies versus 3. If I try to rank them by performance...
1. Raging Bull
2. Taxi Driver
3. The Aviator
4. The King of Comedy
5. Cape Fear
6. The Wolf of Wall Street
7. Shutter Island
8. The Departed
9. Gangs of New York
10. Casino
11. Goodfellas
By movie...
1. Raging Bull
2. Taxi Driver
3. The Aviator
4. Goodfellas
5. The Wolf of Wall Street
6. Shutter Island
7. The King of Comedy
8. The Departed
9. Cape Fear
10. Gangs of New York
11. Casino
And maybe that's a generational thing where I am responding more to DiCaprio's recent body of work and seeing his movies in a theater with no preconceptions.
The film history lover who respects their influence wants to give it to De Niro, but my gut and how I feel tells me DiCaprio. And yet De Niro ranks higher on both lists... so I guess I gotta go with De Niro if only because the Raging/Taxi combo goes higher than The Aviator.
Damn you, DH!!! I thought this would be an easy morning and now I'm overanalyzing with lists.
EDIT: Forgot about New York, New York.