Unless Dick has significantly improved since Bruce died, Batman stomps this. He knows how Dick thinks, he has more weapons (and is better at using his), he knows what skills Dick has (since he gave most/all of them to him), and he has greater strength, strategy, skill, and experience (though not by the margin people tend to think -- it's only about three years, out of 15-20, but still) -- not to mention that Batman probably has a closet full of plans of how to handle Dick under every conceivable set of circumstances. Dick definitely has agility and maybe speed (barely) -- but even on his best day, if it was also Bruce's worst, this would be a long, one-sided fight in the Dark Knight's favor. Not to mention, unless morals are off (always makes fights less interesting, and wasn't mentioned) Dick is more likely to hold back than Bruce. Batman vs Dick and Tim would be a good fight (not sure even The Batman could come out of that one the victor). Everything I just mentioned ignores the fact that, even without having raised, trained, etc. his opponent, Batman's one of the top strategists in DC. We're talking about someone whose plans took down the Justice League, successfully restructured Gotham's underworld as he'd predicted, and even beat Darkseid at his own game, on his own PLANET. Batman's also more likely to get into Dick's head than vice-versa (well, he'll get in sooner), and we know what he can do once he's done that. Batman wins. Finally (a lot of fights seem to go against him on this site).
In response to the Jason Todd comparison, Todd as the Red Hood managed to ESCAPE a couple times, and once Batman saw who Jason was, Batman held back. Bruce then showed Jason what a true down-and dirty fight would be like in the last pages of UTH part 2, after realizing that he couldn't afford to hold back (and destroyed a bathroom with Jason's face, and KNOCKED JASON THROUGH A WALL!
Love that storyline.
Batman then makes a lengthy speech about how Jason's so far inferior that he could never match up (though I'm sure he was exaggerating/being somewhat figurative), and tries to reason with Jason. Then Jason does the "shoot me in the face" thing, and Batman bests him AGAIN (this time, simply outsmarting him). Batman's troubles with Jason were purely personal/moral (Todd would kill), not combative (you know what I mean). Again, I think Batman curbstops Grayson to a fine pulp, in part because Jason's considered to be close in skill. The only reason this would be close is if Batman seriously holds back (he understands Dick far better than Jason; Dick isn't so morally ambivalent when fighting; and Dick probably wouldn't be as motivated to defeat Batman as Jason was, since Jason had something to prove to Bruce -- and himself).
Batman wins.
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