A potential battle between Iron Man and Batman reminds me of the final story arc during Stephanie Brown's brief tenure as Robin, which is collected in trade called
Batman: War Drums. In this arc, the duo twice encounter an assassin named Scarab, a skilled martial artist who wears an advanced high tech battle suit. This new dynamic duo is completely unprepared during their first match, and frankly get their asses handed to them by this new villain who they hadn't previously meet and was much more of a threat than was previously anticipated. Batman then does what he does best: pulling himself back up, learning from his past mistakes, and fully preparing for a re-match in his own terms. More specifically, he dons his own special high tech version of the Batsuit and essential becomes Iron Bat!
I am also reminded of an even more famous moment in the annuals of bat-history in which Batman also dons a special high tech Batsuit and engages a far more powerful enemy--who can fly and shot "laser blasts" like Iron Man but is moreover even more powerful than Iron Man--in a battle Batman won largely by fully preparing for it in advance and utilizing every conceivable advantage: the stand-off between Superman and Batman at the end of Frank Miller's
The Dark Knight Returns! In fact, earlier in this very story-arc: Batman and the Mutant Leader essentially fight to draw in the mindless slug-fest that was their first encounter, after which Batman again learns from his past mistakes and prepares for rematch on his own terms that he resoundingly wins! In both cases, prep'ing an arena of his own choosing and using superior tactics to compensate and even negate his foe's superior physical prowess.
Batman also donned advanced high tech suits not dissimilar to Iron Man's in
The Night of Owls and
Kingdom Come.
These stories, and the
JLA: Tower of Babel arc mentioned above by
@Leeroy_MY, persuade me to give Batman the edge over Iron Man if they were able to fully prepare for their encounter in advance!
Granted, Iron Man has also demonstrated that he develops special strategies and tech should he need to combat a specific person more powerful than himself, namely the Hulk-Buster and the Thor-Buster. Regardless, I suspect that Batman is the superior technician with access to comparable technological advantages. (Though I also quite like Iron Man, I'm much less versed with him than with Batman and I welcome a bigger, more well versed Iron Man fan to comment further on Iron Man's skills as a strategist or if there are specific stories that suggest that Iron Man would actually have the edge.)
However, if this were a random encounter in which Batman and Iron Man weren't specially prepared and equipped with only their standard suits and tools: I'm honestly not sure who would win!
In either case, even when I give Batman the edge for a well-prepared encounter: this would be an epic, fairly evenly matched duel that it would be quite interesting to read!