I would rather write an amazing poem as the latter sounds rather creepy, actually! I do not know how I would respond to someone writing a poem about me, but I am pretty sure the reaction would be extremely negative. I am not someone who handles compliments very well, and if it were someone that I did not know very well, I would probably be pretty angry.
It is interesting to me that the question used “muse” in the more traditional sense of “someone you are inspired by to create” for whatever reason. Another way I have seen it used is by writers who have the kind of active imaginations where their individual characters have minds of their own. That is to say, they will say things like, “I have just now discovered how much of an unreliable narrator Stone is,” or “Okay, thanks to Dave, I have spent the past two hours on various sites looking up DJ equipment. Thanks Dave.”
(This can be occasionally disconcerting or even confusing. On one occasion, I became confused about whether someone was talking about the characters for her Nanowrimo or people she knew who were not inside her head. On that occasion, I think I pretty much confirmed her suspicion I was a space cadet.)
I tend to prefer the idea of an imaginary-friend type muse over a real person that one considers a subject/muse. This is because if you have a real person as a muse, how the heck do you know that whatever it is about them you think is muse-worthy even real? Isn’t having someone be your “muse” putting that person on a pedestal? I think an idealized version of a real person is much less real compared someone inside your own head that you made up.