As a long time fan of both characters (through both their moments of greatness and their moments of git-ness) I’d like to offer my two cents worth to the debate:
It kinda depends on what kind of fight we’re talking about whether or not Tony would last more than ten seconds
If we just shoved them in a wrestling ring type set up with no gear and let them go ham on each other Bruce would win in a matter of seconds. Tony is a twig and highly breakable, Bruce is a highly trained combat fighter who’s built like a brick wall. Tony might get one hit in if Bruce felt pity for him but otherwise he’d be out as fast as Guy Gardner that time Bruce hit him (ie in one punch, for those not familiar)
If we put them in a Huger Games style arena (still with no gear) they’re both closer to their element. Tony’s main strength outside of the suit is his ingenuity and ability to use his surroundings to his advantage. Bruce’s main strength in general is pretty much the same, except he’s more likely to plan ahead rather than build a makeshift weapon and charge his opponent. Bruce would still win but it wasn’t a one sided fight this time
If we gave them their gear then Tony would have the upper hand in terms of strength and firepower, but his main weakness is impulsivity. When matched against an opponent able to make rock solid plans on the fly and predict your actions based on information gathered even just during this fight his recklessness makes him fall short of the mark (although this trait may also be an advantage in a way, given that not planning your next move makes you harder to predict). Batman would easily be able to identify his failings (both in his fighting style and the suit itself) and formulate a plan to take him down. Or just fire an EMP at him if he didn’t have time to humour him
I’m also gonna include a few things that aren’t technically fights just for fun:
In a fight over who could keep their identity secret the longest Bruce is the clear winner. Even if it’s not super hard to put the pieces together that he’s Batman he tries his hardest and has yet to accidentally reveal it to the world. Tony can’t keep his identity secret for more than ten minutes without literally holding a press conference announcing it
In a fight over who is more sane Tony would win by a very small margin. Very small. This is the only time he’d beat Bruce and even this is closer to a tie. Both of them need to talk to a therapist
TLDR: Bruce would win in any situation