Just remember, while you get the 'that must suck to have a kid near Christmas' for the entire pregnancy....your child will forever get 'ooh a Xmas eve baby. Do u only get one present?' EVERY time they have to say their birthday. So you get off relatively easy!!!
My advice is to make sure you celebrate both events. We rarely did anything xmasy on Xmas eve because it was my bday. I always got separate presents. And birthday presents were not allowed to be wrapped in Xmas paper and I hated getting cards that had bday and Xmas wishes in there. Two separate days people! Apart from that it doesn't bother me. I loved that I never had to go to school (always had to go to church tho) and my parents were never at work in bday so that was awesome. And we always left out some of my bday cake for Santa!