Batman is not defeating Iron Man. Let's just get this out of the way. Nothing short of chaining Iron Man to a wall and being shanked repeatedly will give Bruce the win. "He knows 127 martial arts," I hear you say. Fat lot of good it will do him when he's karate chopping a suit of armor that takes hits from the Hulk. "He has gadgets, " you say again. Nothing in Batman's arsenal save something that has an explosive output above that of a nuke will hurt Iron Man, and he can easily recover from that. "He can prep for him, " you desperately try. Prep for the guy who preps for abstract entities like the Phoenix? Yeah no. So let me just say again, the Bat will not be beating Iron Man, prep or otherwise. That was never the point of question anyway.
The problem with DC's heroes is that you can't relate to any of them. The same is true of Batman. You can say Bruce is just human all you want, but in my book no human is capable of mastering 127 different martial arts, studying a plethora of degrees and still be in his mid-30s.
Iron Man, on the other hand, is more relatable. His weakness is every human's weakness: the mortality of man. A diehard capitalist who is faced with the truth that he is not truly invincible, decides to become an altruist, a hero. You can sympathize with this development in character. Whereas, on the other hand, we still question Batman's choice in his sidekick's costume.
Iron Man is also a logical person. If it's better that a villain no longer remain alive, Tony will make sure he isn't. Whereas for Bruce, god knows how much collateral damage has resulted from his twisted and misplaced sense of justice and morality. By allowing his rogue's gallery to surivive time and time again, he has unwittingly allowed Gotham to become one of the seven circles of hell.
Regardless of whether you think Tony or Bruce is richer, the external benefit of their riches is more prominent in the MU. Tony creates new elements, furthering scientific research. He heavily influences the creation of a Dyson spehere around the sun, harvesting solar energy and even weaponizing the star. It goes without saying, Tony also donates his wealth to charities and whatnot. Meanwhile, Bruce localizes his wealth to just Gotham. And even then, Gotham remains a hive of scum ans villainy.
So, to conclude, Tony is better than his wealthy counterpart not by being a better person, but a more relatable one. People can connect with Tony's choices and actions, but no one will accept that a speedo and a shirt is the best uniform for your sidekick.
It's apparent that they are both billionaires with and inexhaustible supply resources and geniuses in terms of weaponry and technology. Despite ironman seemingly having more advanced technology, bat man has a few traits and accolades that tilt the odds in his favor. For one thing he is a master of every fighting style and a master of stealth and tactic, at least to a greater extent than ironman. Also, while his weapons are not as advanced as ironmans, he does have access to a variety of vehicles and gadgets, not to mention his capability to devise new weapons tailored for the defeat of ironman. Finally his combination of intuition when in battle (an effect only compounded by ironmans arrogance and dependence on superior weaponry) and shear battle experience and technological capacity make him just a notch higher than ironman in a one on one fight.
Batman can handle any situation even if it means playing dirty. A lot of times in the Justice League, all Batman does is let his power gifted team mates handle everything while he assesses the villains weakness and wait for the right time to strike. Many people say "Batman is only a man in a fancy bat suit with cool gadgets, how can he possibly beat Iron Man." Well, in The Dark Knight Return, Part 2. Batman had a suit that goes toe to toe against superman.