Let's remember here that Wayne and Stark both qualify as badass normal with no super powers, both are super-genius gadget inventors, and both are super rich, also both have had major motion pictures and animated cartoons so neither has any special "He's much cooler" or "Been around longer" edge. Iron man doesn't have some secret weakness nor even a secret identity to worry about, Batman has the latter and usually when he's taken on seriously-pumped up bad guys he's relied on them having the former.

Honestly I don't think it would even be a contest if Iron Man started the rumble, Batman's cool but he's in the realm of normality and doing the King Kong vs Godzilla super-size routine on hero v hero or 2 heroes allied in a crossover always leaves a bad taste in my mouth, 'don't piss of either fan base' and no sense of scale, justice league of superheroes kind of stuff. You can make a case for almost anyone beating the other guy if they had some prep time, krpytonite sniper round kinda thing.

Batman's at his best as highly intelligent and motivated normal guy whose a very smart detective, there are go-go-gadget versions of him that are basically identical to Iron Man but I don't think it has the right flavor. Dump both normal versions in a cage match and it would be about 10 seconds.