You’re assuming that both men were approaching the Constitution with good faith–with an intention to exercise only the power the Constitution was supposed to grant the government. There is no reason to believe that Hamilton behaved that way.
Hamilton said in The Federalist that the Federal Government would have a few defined powers. Once he was secretary of the treasury, he seems not to have found any way in which those powers were few or defined.
This isn’t surprising. In fact, much of the discussion in the ratification contest was over the likelihood that federal officials would grab at more power than the Federalists were saying the Constitution was going to give them. The Preamble to the Bill of Rights, which you can find in the Appendix to Tom Woods’ and my Who Killed the Constitution?, says that was the reason for the Bill of Rights.