I usually serve both.
The pig is the solar animal related to the mid-winter festival associated with the Norse myths where Odin wore a freshly flayed reindeer skin and dropped gifts down the chimneys of his followers. The turkey is the solar animal associated with the mid-winter festivals of native, north and south, continental Americans. If we serve goose, we are remembering the the solar animal associated with the Celtic mid-winter festivals.
Like all Christian festivals, Christmas has Pagan roots.