Eh, not really.
The three most important fights between the two are pretty clear on that. In one, Superman, under the control of Max Lord, practically beat Bats to death without really trying. In the infamous DKR fight, Supes had been weakened by a nuke, missiles, sonar weapons, Bats had power armour, kryptonite, etc, and Supes was holding back. And in Hush, Bats, with a Kryptonite ring, basically breaks his arm punching Superman, and he states in his own monologue that if he wanted to, Superman would curbstomp him regardless of Kryptonite.