I think they're both "indie" film actors who have been caught up in big box-office roles. Depp seems to be the go-to guy for what will pass as fringe in Hollywood, and DiCaprio seems to be the go-to guy for what will pass as glamorous in Hollywood. I think both assumptions are misleading, though.
It's difficult to honestly pin down who really is the better actor, as both have truly impressive resumes with a variety of roles that show their range in acting. Plus, they're both still young with years ahead of them as they enjoy their prime.
The Quick and the Dead, Gilbert Grape, Marvin's Room, The Departed, Catch Me If You Can....and I SO want to see The Great Gatsby....I don't think it's a slam dunk for Johnny Depp. But personally, I give Depp the nod for now. And it's ONLY because he made the role of Captain Jack Sparrow that solidified the POTC franchise. So, skill-wise it's a dead-heat. Box-office draw, though, I think goes to Depp.
In time, though, if Leo keeps this up, he's bound to pass up Depp, given his talents in narration, and especially if he gets over himself and takes up directing. I would then rank him right up there with the modern-day Orson Welles, given his potential in the film industry.