Which branch of goverment consuls senate or assembly had the most power

The consuls had the most power - - once they were elected. It was the assemblies who elected the consuls, so they had the most power as far as electing the consuls. However, the candidates for consul (or any other position) came from and were nominated by the senate. So all the bodies of government were interwoven and no other branch had more power than the consuls.

It is congress, the president can't actually do something like make a new law without congress's approval.