No. Christmas Day and New Year's Day are never on the same day in the same year. Christmas Day is always one day in the week later. New Year's Day in 2025 will be on a Wednesday and Christmas Day will be on a Thursday. A week after that, New Year's Day of 2026 will be on a Thursday. It is the Christmas Day of one year and the New Year's Day of the next year that are always on the same day of the week.
Christmas falls on Sunday in 2016.
Christmas Day is great no matter what day of the week it falls on. When it is Christmas Day the day is completely different to any normal day of the week, so whatever day it is doesn't really matter.
Christmas Day 2010 is a Saturday.
Christmas Day in 1940 was a Wednesday.
Christmas Day will be on a Sunday in 2011.
Christmas Day will be on a Friday in 2020.
Christmas Day in 1981 was a Friday.
Christmas Day will be on a Wednesday in 2013.
In 1968 Christmas was on Wednesday.
New Year's Day and Christmas Day of the same year never fall on the same day. The 1st of January 1945 was on a Monday and the 25th of December 1945 was on a Tuesday. That is completely normal. A week after Christmas Day is New Year's Day, but that is New Year's Day of the following year. So Christmas Day 1945 would have been on the same day of the week as New Year's Day 1946, the next year. In the same way, Christmas Day 1944 and New Year's Day 1945 were on the same day of the week.
Christmas Day in 1914 was on a Friday.