For the Dec 9-10 threat, the key difference between the GFS and Euro is the position/strength of the HP over eastern Canada leading into, and during the event. At h5 there is a vortex that gets pinched off underneath between the ridge over eastern Canada and the developing NAO ridge over Greenland on the Euro that is absent on the GFS. This feature increases confluence and enhances HP at the surface, which brings colder air south ahead of the approaching wave, and forces it to track further southward with redevelopment along the coast. The vortex sort of acts as a westward displaced 50/50 low. The CMC has this feature too but further north and somewhat weaker, thus its solution is in between the GFS and Euro.
Look at the difference at the surface leading in-