I think the first time they fought was 2 minutes after Cap awoke in the present, to prove he was the real deal; Iron Man and Cap also fought after the Chameleon set them up; first time after that (I doubt it was) I remember was during 'Armor Wars' when Tony took out the Guardsmen; they disagreed over the decision to kill the Supreme Intelligence during 'Galactic Storm'...
But none of that compares to what happened during 'Civil War', of course.
I think their conflict during 'Armor Wars' was more important, because that essentially set the two of them on the road to Civil War in the first place. This is where Tony vs Steve really starts.
Whilst a great story, Tonys behavior in that story was just all kinds of wrong. He attacks his allies, is responsible for the death of a youth when he chooses to tackle the controller in a public place, illegally invades a foreign nation and kills one of its national heroes, disables the guards in a prison resulting in the prisoners escaping and numerous deaths, and attacks Cap when he tries to stop it.
That story embodies all of the personality faults of Starks that would be the reason for him clashing with Rogers in future.