Being one of the Batmans...Batmens?...Batpeoples? makes it easier to choose because the they're all pretty much punchy street level heroes.
So my first choice is Pulp Cthulhu and you can easily moderate how gritty vs pulpy you want it, the pulp talents in the book are in line with that street level vibe. Since they're not fighting the mythos you can just ignore the SAN mechanics...or use them to showcase what a nutjob Bruce was... Also CoC lends itself to the skills, investigation bent that Batperson comics like to have.
If you did want something more superpowered you could pull the super powers from the Achtung Cthulhu supplement Elder Godlike. I never tested them out but I have wanted to. They are just a step above street level, but not quite Superman powers.