I would say that Batman is better if for no reason other than he is human and doesn’t rely as much on Deus ex machina or other hokiness to do what he does.
Batman often achieves victory through cunning and is far better suited for instances where a heat ray or brute force won’t help. Want to solve world hunger? Yeah, Superman can plow and plant a field in a few minutes and feed a few people, but Batman can come up a far-reaching plan to grow crops in perpetuity and distribute them to millions while creating jobs that help people elsewhere in the process. Want to solve a mystery? Go with the guy who has skills in forensics over the guy who just flies to Lex Luthor’s office and shakes him down.
And speaking of shaking people down, Batman is better at that too. Superman may be strong enough to rip you limb from limb or melt your face off, but he is too much of a boy scout to be intimidating. On the other hand, Batman isn’t afraid to rip out a person’s spleen and beat them with it. Of course, he hasn’t actually had to do that since he scares people into submission without having to do so, which should tell you something.
Batman proves what is humanly possible while Superman demonstrates that humanity is inferior. Batman gives us things to aspire to, like great but achievable cunning, agility, ingenuity, etcetera while Superman makes us feel like putzes for not being able to fly, lift tanks, or shoot rays from our eyes.