We've spent the last 2 NY at DLP and both were beyond busy. In 2017 we spent 4 nights, travelling home on the 2nd Jan, this year we went for 5 days because it had been so busy the year before!!
I don't think it makes much difference when you go during that period, some of the waiting times today were longer than Monday. Personally I prefer before NY because Christmas is just a little bit fresher in the mind.
Be prepared for busy, use Extra Magic Time, Fastpass, Lineberty and plan for long days. We had amazing times both years and are planning to do the same next year.
This year we stayed at Davy Crockett, were up before 6.30 most mornings and back very late most nights. Used EMT to get through some of the busier rides and Fastpass later in the day, leaving the middle of the day to wait for character meets and just wandering round the park, I'm a sucker for the 'architecture'. I was put off paying for NY in Disneyland Park this year as there were 5 of us and £87 each was a stretch too far, so we spent the day in The Studios and stayed till close at 12.30am. All the rides were open so there was plenty of time to see /do every attraction - and I (not so) secretly love The Studios so was like a certain Bear with honey.
We arrived home at 8.30pm last night and I went to work today knackered but will definitely do it again and again, despite the crowds.