Goa is a place full of sunny beaches, nightlife, flea markets and lot of history to explore. It's am ideal spot to visit in Summer. Manali is called as Lovers Paradise which gives viewed of the magnificent Pir panjal ranges. Though best time is to visit now, for u get to see the snow. I would say Goa since new year is nearing.
During the months of December and January, Goa is preferred because the climate is pleasant there. In Manali, it can be extremely cold during these months which some people find difficult to travel in such conditions.
Both are great places but visit according to the weather.