OP answer
Not really since it's often mitigated by Superman being the best friend who knows Batman best to snark back, make fun of his brooding nature, or pointed out how his ideas are insane, which he does anyway because he's the best brain in the room, basically acting as the wiser, patient, smirking older brother dealing with Bruce's goth drama.
I only read Batman/Superman, Superman/Batman, and Super Sons though, so their dynamic is more equal. I haven't read classic Justice League stories and what I saw from Justice League Unlimited I don't really like since it seems that series is Batman and His Bitches.