Zaitzev was real, Koenig is Hollywood fiction.
No, Koenig was a real individual. He was head of the German sniper school. He was a full colonel. He was sent out when Sixth Army Command asked OKW for a sniper to go after Vassily Zaitsev, a Russian enlisted man who was making a name for himself in the streets of Stalingrad.
When Koenig arrived, both armies knew that a duel was on. It was one of those great mano a mano battles that one saw very little of in the Second World War. Koenig's misfortune was that he made more mistakes than Zeitsev.
Enemy at the Gates was fictionalized to make Koenig more murderous than he actually was. Koenig, for instance, murders a young Russian boy when he finds that the boy has been passing information to Zaitsev. I don't recall any event like this ever happening.
Koenig was a professional soldier and an aristocrat. He took pride in his work, which is why he was head of the Sniper School. I seriously doubt that he was the kind of individual who would murder a young boy.
Zaitsev was heroic enough. There is no reason to enhance his heroism by running down the character of his opponent, who was killed by Zaitsev in the end, anyway.