It all depends how you write it. Where are they meeting? Do they know they're fighting in advance?
In order to avoid accusations of prep-time batgod bias, it's best they meet in one of their cities without prior knowledge they're going to fight.
Your best arguments are:
-While both are geniuses, Batman has demonstrated greater wit against more clever foes with less physical capability.
This means in a fight where Ironman is constantly heat-seeking and chasing a guerrilla-warfare Batman in the streets, Batman is likely to walk the head-strong Ironman into a trap, by luring him into an enclosed space or unstable building, or using the element of surprise by obscuring his heat signature somehow. This isn't to say Tony doesn't have a strategic mind as well, we know he does, but he's more secure in direct confrontations. Batman took down the entire Justice League ffs.
-Iron Man's suit, while Tony's greatest strength, it's his greatest vulnerability.
If it stops working, he's trapped in it. We've seen EMP blasts turn Iron Man off before. The writers have gone back and forth on this concept it seems so as to not make it so simple, but I think it's safe to assume some kind of electrical interference will affect the suit, and that Batman has that technology in one of his readily accessible vehicles, if not on his person.
-With prep, Batman has these advantages in strategy (not out of just being smarter, but having to be more cunning without the advantages of a versatile armored suit), but has also been shown to make power suits just as strong (if not as versatile and mobile) as Tony's.
Whether it's against Superman, Darkseid, or the League of Assassins, Batman has busted out the big suits plenty of time. The insider suit is alsoridiculously strong, incorporating limited use of the powers of the mean JLA members.
Now, is this fight to the death? Or until debilitation/capture?
The way I imagine it is like this:
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Batman is on patrol, perhaps in Gotham, perhaps in another city where Iron Man is doing business. Maybe an abandoned neighborhood where Ironman won't be afraid to use his artillery. Oracle tells Batman that local radars are picking up something huge and metallic coming their way. Tony hacks onto their frequency and tells them to keep out of whatever it is they're competing to get as he zeroes in on precisely where Batman is.
Batman, already likely wearing material that at least partially obscures his heat signature, throws every smoke bomb he has and fills up a whole block with it. Tony rolls his eyes and starts to cut off the exits he can detect with the suit with missile fire or his flamethrower.
Batman sets up his cowl onto the back of the chair with a small fire burning on it in the building with the sought-after thing, and sets up on the cieling, maybe shirtless to get cold while he meditates. Iron Man walks in talking about how futile it is to run. He grabs the cowl, and Batman descends from the ceiling, hitting Iron man from above hard. It hits him solid but Ironman just swats Batman out into the hallway. Batman then detonates the charges he put on the ceiling and the building collapses on Iron Man.
Batman tries to make a run for it, perhaps with the thing they were both looking for. Iron Man is right behind him, flying, now angry. Batman throws like 5 explosive batarangs, which do nothing to Ironman. Ironman blasts batman with his hands. Batman falls, really hurt, holding his ribs. He goes for his belt, but Ironman grabs his hand hard, hurting it, and strips him of the belt. Tony looks at it while the suit breaks down its contents, makes a disparaging comment, but there's a small red light beeping in one of the compartments.
All of a sudden, there's a swoosh from above, and an EMP bomb. It drops, and Ironman's suit starts to glitch and falter. Batman grabs a cement boulder and goes ham. Back of the knee, gut, and the head, which knocks the helmet off (or at least partially off).
Finally, Batman gets all up in his ear and says something like "Don't get in my way again. Or next time, you'll run home with more than a broken toy." After a minute, the suit is back online, and Tony is looking around, alone, gritting his teeth hard in utter frustration and anger towards his self.