It's narrative that let's Batman even put up a fight with Superman.
Let's just take TDKR, he wasn't just in a metal batsuit.
Both are older, let's get that out of the way.
Superman took a nuke exploding in the face, it really weakened him, b/c when they confronted, Batman sent (the equivalent) of drones to attack/pummel batman.
He had Carrie in a tank fire and hit batman with enough force to sink a battleship.
He fired a sonic gun (i'm guessing to mess with his equilibrium) and the Metal Batsuit is powered by being tethered to the city's powergrid.
Every action and anticipation was planned b/c Batman knew Superman, he knew what he would do and how he would react, from decades of friendship/battles.
Right down to synthesizing his own man made kryptonite fired by a 1 armed arrow.
And then messing with Superman's head by targeting his heart(not his real heart, but that he cares, cuz he hears Batman's heart give out), cuz this was the most Batman could do.
Trick Superman, he could never beat him, he had to rely on the hope that Superman still had feelings (cuz he's a fucking alien) and cared that Bruce died fighting.
And TDK narrative does NOT shine light on Superman, this isn't a way to give Batman a dirty win, no Superman is the worst and dumbest government lackey, he is the lowest scum in TDK.
Just like this battle doesn't end the way every thinking human on earth would believe.