How can a regular flight instructor compete with any more senior instructor? When given a choice the student is clearly going to pick the more senior one.

Hopefully it's not as clear as that.

For a Part 61 school, a "chief" CFI has no official FAA role. He is really just an effort for the flight school to broadcast a more professional image and, as others have said, has a role that varies with the size and other aspects of the operation.