No, not dukeing it out.
The Dark Knight mus go to Arkham Asylum to question Lecter on the whereabouts of a former patient, Sszazss. It is imperative to prevent mass murder in Gotham City.
They do the Quid Pro Quo routine.
Who bests who?
Batman loses, if he’s prepared with fava beans and a nice chianti.
Lecter will clearly win. Batman/Bruce Wayne is fragile enough as it is. Lecter will see through Batman’s disguise, figure out he’s Bruce Wayne, and then all the wounds will open up again for Wayne.
Holy Twisted Psyche, Cecil . . .
Um, I haven’t read Batman in over a decade, but I’ll give it a shot anyway . . .
The good doctor forces Batman to confront the demons from his past, and after a couple dozen very dark comic book frames worth of catharsis, Bats is healed. Bruce Wayne, now at peace with himself, his past, and the world no longer needs to don the mask and cowl and retires the Batman identity. The authorities track down Sszazss and kill him, but Hannibal gets away. No longer protected by the world’s most obsessive and psychologically damaged hero, Gotham City finds itself terrorized by the worst serial killer to stalk its streets in living memory. The Gotham City Symphony Orchestra soon finds itself short a flute player, but there’s one hell of a flower arrangement at the late musician’s funereal, courtesy of the Wayne Foundation.
So, for both Batman and Hannibal, it’s a win-win situation.
Hannibal is smart as hell but I find that sometimes people give me too much credit. I’m saying Batman out smarts Lecter and gets what he needs out of him in only a couple sessions. Besides people forget the fact that Batman faces twisted geniuses every night (Joker, Two-Face, Riddler).
Like for example once Ras Al Ghul tried to open Batman’s wounds similarly to what Mehpisto and Rabid Child suggested but it didn’t work. Hell, Ras Al Ghul even dug up the graves of Batman’s parents and tried to revive them in the Lazarus Pits but once again Batman managed to keep his cool and defeat Al Ghul.
And add that to the fact that Ras Al Ghul has been trying to crack Batman for years and years. Do you think Lecter could even come close to that in only a couple weeks while he’s locked in a prison cell and without as many resources that Al Ghul has (besides Ras Al Ghul is smarter than Lecter).
Damn it. It should say people sometimes give HIM too much credit, not me.
Ha! The secret’s out now . . . I hope for your sake that Batman’s not surfing the net tonight, Doctor DK2. Don’t worry . . . every evil genius slips up sooner or later. 
Who knew there was Internet access for the patients up at Arkham?