They are co-equal. But, each has unique powers. The president can appoint cabinet level offices. But he must get the Senate's advice and consent, before any can be sworn in and serve. Only the House can introduce taxes. The Supreme Court ruled, and a similar ruling recently confirmed this, that the President and the Executive Branch must answer Congressional Subpoenas. The original ruling was against Nixon, who resigned a shortly after being told that he had to answer to the House of Representatives in his Impeachment. Separate, equal, but not exclusive or immune from action.