The two holidays are almost integrally linked in Western culture. Is it a coincidence that they're so close, or was there some kind of effort to put them next to each other?
This answer to a similar question by u/WelfOnTheShelf gives a good history of the date we consider "new year".
Regarding them as "holidays" I cannot find an answer here, nor one on the history of Scottish Hogmanay but suggest that as maybe an area of further interest for you.