It all depends on whether each character is granted their usual "outfit," plus all of their presumed "talents," and personality etc. Because if both men were simply in street clothes, it's not even a contest, Bruce Wayne would beat Tony Stark pretty fast.
But if each man stumbled across the other by accident, unexpectedly and unprepared to face one another, but having to keep fighting one another until one or the other wins, with Batman having only the things he usually carries on patrol and Iron Man in his suit with no special preparations either, I have to overcome my bias and admit that Iron Man's power is too much for Batman to hold out against for very long.
We'd have to grant Batman the "pseudo-superpowers" level that he seems to get when he's fighting as part of the JLA (when cast alongside Superman and Green Lantern etc, Batman tends to be attributed with a lot more strength and speed than an actual mortal could possibly attain; it's the way to keep him relevant in stories with indestructible aliens and magic, basically), in order for him to possibly be able to keep dodging Iron Man's blasts and weapons. He couldn't do much to harm Iron Man, either, since the armor is nearly indestructible. Iron Man's speed, reactions, and sensory abilities all take on superhuman levels, and with his armor linked to his mind, this means he can act and react at the speed of thought -- enhanced by the speed of computers.
One thing people unfamiliar with Iron Man don't realize is, his armor records and analyzes every opponent he's EVER battled, increasingly creating better and better actions and reactions, anticipating moves based on every nuance and previous event etc, so that he even was able to best Captain America in hand-to-hand combat (CA however had a trick up his sleeve, he'd prepared in advance for Iron Man and had gadgets to shut down the armor plus the help of other superheroes in the fight; but just face-to-face, one-on-one, the truth is that Iron Man was superior to CA in the fight). The cumulative effect of the armor, computer systems, weapons systems, Stark's mind being like a super computer, and his fighting skills being literally based on decades of battles against practically every villain and superhero and thus giving him the greatest battle-training preparedness of any character in either Marvel or D.C.
HOWEVER -- This is all assuming Batman didn't know about Iron Man until this moment and never tried to prepare for the moment, and didn't anticipate the coming battle and have things on-hand in case the fight was imminent. If we are letting Iron Man have his armor and thus inherently be prepared for almost any eventuality possible with ANY other character, in fairness we should probably also consider a scenario in which Batman at least was aware of Iron Man's existence and took action to prepare in case he ever ran across him in battle.
In that case, Batman would almost certainly be the victor. I say this because he'd quite simply have spent the same amount of time preparing for this fight as for a fight with Superman, and thus would've had Wayne Enterprises spend billions of dollars to slowly infiltrate Stark Industries to monitor, hack, copy, analyze, etc everything and anything related to the Iron Man armor. Batman would probably have satellites in orbit for the sole purpose of following Iron Man and alerting Batman if Iron Man got close, and those satellites almost surely would also contain technology designed to do what CA's S.H.I.E.L.D. gadget did to disrupt Iron Man's armor (I have no doubt Batman's technology is better than S.H.I.E.L.D. in that regard; but I could be misremembering who gave CA the gadget, I've not read "Civil War" again in many months). The follow-up to that would be satellite-guided missiles to shake Stark inside the armor and rattle him a bit, while Batman takes advantage of the precious time to unleash a series of weapons and moves to knock Stark out inside the armor before it reboots itself.
Questions about whether Batman can beat this or that character always hinge on Batman's "disaster preparedness" planning being a factor. It's a major part of his persona, and when it's taken into consideration, it's hard to ignore that he has detailed plans for beating and stopping every single superhero and villain on the planet. Literally, there's a whole story about this very fact.
More questions on superheroes:
Follow Quora on Twitter: www.twitter.com/Quora