Many Constitution Party members are libertarians, in some way, shape or form. However, there are very few Libertarians--if any at all--that would comfortably identify themselves as [subscribing] to the Constitution Party platform.
However, the biggest difference between the two parties, and one that is the best manifestation of the diametric difference of philosophies on the role of government in society, relates to the issue of gay rights.
As the Constitution Party members would say, "Amen."