He's fought Batman and such, but one that comes to mind was during a body swap storyline. He had Batman's body, and Superman had his body. He outskilled Superman, but Superman still managed to win via tenacity.
He also fought Mr. Terrific, and Michael seemed to be at least his equal or in possession of a small edge, until Kobra spit poison at him.
He, apparently, has one HtH against Batman (going by wikipedia here, and pre-Crisis), but most of the time he's a "put up a good fight but loses or cheats to escape" foe.
Cass stomps.
Mr. Terrific knows something like 7 martial arts, which makes him good but not anywhere near Batmans class, yet Kobra still struggled against him. And I can't see Superman with human stats beating Batman like he beat Kobra, even if imo he's a better fighter than people give him credit for.