They both had reason to lose their temper. You're just too biased to acknowledge it. I'm not immune to it either. So was I at the time I read that first Action Rebirth issue. I was still upset about the changes, I was in no position to be rational about it. But I can admit that now. In the end, its just as reasonable to have an attack on your city make a Superman rage-filled. And that's what he thought was going on. He was incorrect, Batman and GL weren't connected to the threat, but that's what he thought at the time and for justifiable enough reasons (and its worth pointing out that Batman GL were just as incorrect as he, they were only there because they thought SUPERMAN was involved. It was one giant misunderstanding). Just like Rebirth Superman was incorrect that this Lex was using the symbol for terror.
Fact is, VERY often Superman's M.O. is to punch first and ask questions later, depending on the situation. All Supermen. Including the pre-FP model. Their "punch first" just never is permanently damaging so he can get away with it. He knows how to control his force.