Superman in Death of Superman even contemplated flying all the way to space to power himself up and prepare a counterattack IIRC, but he decided against it because he needed to stop Doomsday from harming more people. They fought across half of the country pretty much, and he just held his last stand in Metropolis to save the city from him, determined to stop him at all costs.
It's a well - known fact that Superman's power has been increasing greatly ever since the end of COIE, in the early Byrne era he was weakened by a 40 megaton explosion, a few years later he took an equivalent explosion while sitting in an island of Kryptonite and was unharmed, and then funneled the explosion and radiation into space. Check out Doomsday Rex where he pwned Doomsday so badly that his bone claws actually broke when he attempted to punch Superman.