I have read the compilation graphic novel with the entire Doomsday battle. At the end of the battle Superman and Doomsday kill each other in a classic "same-time" final blow. It was my understanding that Superman could only be seriously injured or killed by Kryptonite. There was never any indication, to my knowledge, that Doomsday had Kryptonite so how did he kill superman?
Spoilers, if you haven't read the storylines in the Superman family of comics that follow the Death of Superman story:
Superman wasn't actually killed during this battle, but nearly was. Thanks to the Eradicator placing his body in a chamber that bombards his body with solar radiation, he was able to eventually recover.
Doomsday was able to accomplish this by being as tough as Superman. In addition, he has the speed and strength of Superman, and was able to maintain an unending assault on him. This eventually wore down Superman, until he was simply physically beaten to death.
Superman, as we know it, is a solar battery of sort; he can store the yellow rays of our sun and converts it to become the fast/strong/whatever that he is. While there hasn't been a real limit of how much he can store, it is a finite amount. This explains why Superman has abilities at a nighttime zone on Earth when the sun isn't out, as the reflected rays off the moon and the miniscule amount from the star in the galaxy are not enough to fuel his abilities.
Having said that...
Superman's ability to convery solar energy to fuel his abilities proved ultimately to what caused his defeat to Doomsday. While he wasn't necessarily 'killed' (as many of his clones/likenessess have equally survived such drastic beatings) Superman isn't an immortal. Take Superboy Prime who by, all intents and purposes, is equal to Superman in every way. Exiled during the Infinite Crisis, had a suit constructed to store yellow solar rays to prevent the possibility of depleting his stored energy. This let him trash the Green Lantern Corps (who may have an unlimited source of power through the power of Will) though doesn't stand up to SBP.
To answer your question...
Superman basically initiated a Kamakazi run on Doomsday. He held nothing back to defeat him. Doomsdays was a genetically-engineered creature that the Titans made to be their trump card, giving him the ability to get use to damage and power, and thus become more immune to it. By the time Superman faced Doomsday, Doomsday had already faced and killed the Titans, not to mention thrashing through several Earth-based military weapons to try and stop him. Doomsday strength and abilities are not based upon a power source, as he was actually created with them. Superman, on the other hand, was fighting at night, against one of his toughtest opponents. When Supes faced such beings such as Zod or Cyborg, he was facing opponents like him; beings that also harvest the energy of the sun; an equal setting. Against Doomsday, Superman is actually on the losing edge; his stored energy is being used faster than it can recover, and Doomsday wasn't about to let the Man of Steel take a breather.
Doomsday was defeated because Superman was using levels of strength as yet unencounted by the creature, breaking through his immunity for vast punishment. But this had an effect on the Kryptonian; he was literally fighting harder than he ever had against Doomsday, taking some brutal punishment himself. This goes to show that Superman, while extremely powerful, can in fact get tired/exhausted; possibly a real weakness besides Kryptonium. Keep him in the dark and have him expending as much energy as possible can lead the Man of Steel for a loss, especially against a foe who can take it and dish it out. Someone, such as Superboy Prime in his lightsuit could very well defeat Superman in the right conditions (if Superboy Prime ever stopped to, you know, use his brain every once in a while).
Well if you all look back at Doomsday's origin, you see he was created on Krypton and was created to defeat any opponent. He is a genetic war machine. Cloned and cloned so he could not be defeated by the same way twice. To put it shortly with both beings being Kryptonian, the had equal powers and vulnerabilities. So that made the fight fair and dangerous to both.