I did not think it was any more depressing or violent than the other Batman films, but Ledger's acting as the Joker brought out the realism of a vicious mind rather than the cartoon type of Joker played by Nicholson. Heath Ledger became this tortured and torturing soul.
I cover my eyes when I know something might be more graphic than I want to hold in my memory.

In comparison, I thought Sophie's Choice was darker and more depressing than this film. With Batman, you always sense the cartoon good guys will prevail in the end.