This topic seems familar... let me elaborate on Balthus Dire's post...
In the Punisher/Batman crossover (the one with Bruce Wayne, not Azrael), they did fight, most notably at the end of the book when the Punisher is about to put a bullet in the Joker, after being involved in a firefight and a lengthy chase.
In the end, Batman shows up, grabs the Punisher's arm as he's about to fire and tells the Joker to run away.
Even though the Punisher had been shot in the arms, and was losing blood, he punches Batman in the face, he takes another swing and Batman shoves him into a bunch of boxes in the alley. Batman tells him to leave Gotham. The End.
That's about it. Their first battle ends essentially in a draw (A collapsing ceiling ended that battle) and the final battle has a wounded Punisher fighting a healthy Batman.
The whole book was pretty anti-climatic.
Chuck Dixon wrote that Punisher/Batman crossover and it's pretty obvious that he wasn't interested in writing a Punisher that was a major threat to Batman, in fact, his Punisher seemed to be more brawn than brains.
I've never been too big a fan of Dixon's later work on the Punisher.
If anything, I'd say that the final outcome really depends on who is writing the book. For example, if Garth Ennis, Carl Potts, or Mike Baron were writing such a crossover, the Punisher wouldn't have come across as a chump and Batman really would of had a fight on his hands.