The executive branch is responsible for implementing the laws that are created by the legislative branch, the purpose of the executive branch is to execute, enforce, and administer the laws that congress passes. I think the power most important in the executive branch is being able to veto, or reject, a proposal for a law, and appoint federal posts.
I believe the executive branch is the most powerful because it largely depends on the president in power, if the president knows how top work the system the executive branch can have immense power. The president has opportunity to appoint Supreme Court justices and can use his influence to shape policy. The president and vice president have a lot of power and the president is commander in chief of the US armed forces.