are the excutive power at the state level and federal level the same?

Answer 1

Using Australia:

Federal Parliament and State Parliament execute different powers, but they both have the same level of power in relations to their allowed powers. They can pass, amend, vote, and reject bills, and can also amend old laws not in the constitution. They can call for a referendum for a change in the constitution, and they appoint the judges in the judicial system (well, the government does anyway).

Answer 2

There are a lot of differences between what a Federal or a state officer can do. The constitution of the United States says the constitution and the Federal laws enacted under it are “The supreme law of the land.” Thus, Federal statutes generally “trump” state or local laws. For example, some states have decriminalized the possession of marijuana – but Federal law trumps that. Usually, the Feds are too busy doing other things to enforce that, but that’s not much to rely on. On the other hand, the Federal government has only those powers the states have delegated to it. Thus, the Feds can’t make local laws unless they can find a federal trigger in one of those “delegated powers”. For example, the Federal statute allowing Federal officials to regulate pollution of almost any body of water was overturned, and the Feds had to show the lake or pond was actually connected to navigable waters of the United States, where the Federal government holds sway.