Take this as you will, but I really do like Batman. I'm probably not telling you anything you don't already know when I say he has no superpowers. Part of his appeal to most people is that he is so very human.
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He is possessed of great intellect and will that he has applied to great personal development academically, physically, and practically. He is also a man driven by powerful emotion, fueling his ongoing war against crime and injustice. Also making his unique lifestyle possible, Batman is possessed of epic wealth. Among other things, that's how he gets those wonderful toys.
Still, there's a segment of the population that doesn't think splitting time between his day job and night job is enough to keep him busy. Some want to see the differences in operational styles and philosophies as friction for fight club action with Superman of all people. Superman!
It's an insane idea in my book. Bad enough to think Batman, known for being as single-minded and relentless as a shark, would find grappling another caped orphan to be a productive use of his time. Add to that, Superman has more power than Batman has money, so you make Batman look more like Wile E. Coyote going after the Road Runner.
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Maybe Batman could just stick to being helpful.
Where I really enjoy seeing Superman and Batman go head-to-head is over on the How It Should Have Ended website. They have coffee and spar verbally. Far more plausible.