When I recently read the fight scene between Batman and Superman in DKR, it seemed very much like Batman was a petty child throwing a tantrum and Superman was an adult that was worried about the child hurting himself. Superman offered very little resistance, and obviously wasn't looking for a fight. During almost every moment of that battle Superman was worried about Batman getting hurt or his heart giving out. Even after the kryptonite gas and getting beaten up, Superman was still more concerned about Batman's wellbeing.
All the while Batman was focused on making this powerful being pay for being powerful and using that power in ways that Batman wouldn't use it. He wanted to remind Superman that a regular person (with millions of dollars to throw around, unlimited access to advanced laboratories, and genius level knowledge of chemistry) could harm him. It kind of felt like Batman just wanted to show that he was the bigger man because he was jealous or insecure.
In the end, Superman discovers Bruce had faked his death and goes along with the ruse, because he didn't feel hurt about the fight and wanted what was best for his old friend.
It seems to me that if Batman had simply explained that his plan was to fake his death and then go into hiding, Superman would have offered to help him with that plan. Instead, Batman goes through with the pointless fight that gains him nothing but more broken bones and the sense that he can beat up a Superman that will stand there and take that beating because he doesn't want to hurt his friend.