The Universal parks do not have reservations, and there have been times recently where they fill to capacity. I would expect that to happen multiple times over Christmas week. I would avoid the Universal parks on Christmas Day and weekend days, and arrive before park opening to ensure you get in. I also would suggest not leaving the park you're in as you may not be permitted back in, if you wanted to re-enter. Express passes for Universal will also be crucial. You can purchase them, but they are included as part of the perks of staying at a Universal deluxe hotel. I believe Portofino Bay will be closed through Christmas, so they would be included for stays at Hard Rock or RPR. It may behoove you to price out a night or two at Universal during that time both for the included Express Passes and because they give on-site guests priority for entering the parks when they reach capacity.
For Disney, we were there last week. No telling what Christmas week will be like, but we did find DHS to be the busiest so I would avoid Christmas and weekend days there. We found Epcot to the be the least busy, so that might be my choice for Christmas Day. If you're staying at a WDW hotel, there is a separate pool of availability for park reservations and its generally easier to obtain what you want when staying on-site, especially if you book early. I suppose its possible for them to increase capacity, but I would not be confident in them releasing more park reservations if one has filled up.