I've read this M.Y. question that explains why tefillin are removed before Musaf on Rosh Hodesh and Hol Hamo'ed.
From what I have noticed in Nusach Ashkenaz shuls, on Hol Hamo'ed Pesach, tefillin is removed before Hallel whereas on Rosh Hodesh, they are kept on for Hallel and removed prior to Musaf. Why is there a difference?
Note: I intentionally did not ask about Hol Hamo'ed Succot, because I have heard that the wearing of tefillin is considered chatzitza when you are holding the arbah minim (four species) during Hallel. Thus, the tefillin are removed prior to Hallel.