It was definitely the emperor who had the decision-making power during the Roman Empire. The consuls became much less important, to the point where it was a largely ceremonial position.
During the Republic, the consuls had a great deal of power. They were sort of like monarchs who reigned for only a set period of time. When the imperial period began, this obviously became impossible. You could not have consuls with the power of monarchs in a system where you also had a monarch. Therefore, the emperor took most of the consuls's power to himself. This extended to the point where the emperors typically gave the consulship out to favorites or relatives as a symbol of favor. There were even times when children were consuls. As can be seen from this, the consuls were in no way as powerful or important as the emperors.