I am from America but I am living in Korea now so I will talk about both countries. In America, I think both are considered equally important even though children would probably prefer Christmas because of the presents. There is a lot of celebration for both holidays. As for Korea, I think Christmas is more important for them. The local Korean people tell me they don't really care about New Year's Day. Instead they seem more interested in the Lunar New Year or what they call " 설날 (Seolnal)."