- Which is most powerful (Governor, US Senator, Cabinet Secretary)?
- Which is most prestigious (Governor, US Senator, Cabinet Secretary)?
- Which is most influential (Governor, US Senator, Cabinet Secretary)?
- If a person has been all 3, post-retirement, which title will they be referred by - most recent or most prestigious? (I have seen Hillary Clinton in the recent past being referred to as both Secretary Clinton and Senator Clinton.)
I can't imagine a way to objectively quantify "power", "prestige", or "influence" so I don't think 1-3 are answerable. Practically, it will be hugely dependent on context. The governor of California is much more powerful and influential than the Secretary of Veteran's Affairs, for example. Whether the California governor is more influential than the Secretary of State, on the other hand, is highly context sensitive. The Secretary of State can be hugely influential on foreign policy (i.e. Secretary of State Henry Kissinger) or can be a minor footnote. To the extent that governors have power and influence, it is almost exclusively on domestic policy making it extremely difficult to compare.
As for what title they'd use, etiquette rules technically say that they'd be referred to as Senator since that is the only title that is a rank rather than a role. Technically, you don't refer to former governors or former cabinet secretaries as Governor or Secretary. Practically, however, these rules are frequently ignored. Most of the time, it depends on what the particular individual prefers or on what the speaker wishes to emphasize. If a newscaster is reporting a story involving Hillary Clinton and Libya, they're probably going to refer to her as Secretary Clinton to emphasize her foreign policy credentials or to indicate that she was Secretary of State during the events in question.