Did Big Bend at Spring Break one year before COVID - never again! The place was packed with college students. Almost no sites were available.
Always do Big Bend over Christmas and this year it was showing "full" on both the web site and on entrance to the park, but over half the spaces were unoccupied because of the requirement for "social distancing" I guess. They've also pretty much eliminated the non-reservation sites so a reservation is needed and unless you book about six months ahead of time you'll probably be out of luck. We did book our Christmas reservations as soon as we could but weren't able to get the spots we normally get every year because there was such a crowd waiting to hit the "send" button on their computers when reservations opened up.
BTW, Davis Mountains State Park is a nice place to stay if visiting the McDonald Observatory, but some of the same problems getting into State Parks because of COVID. Need reservations, need to be made WAY ahead of time, and the parks are usually almost empty because of the COVID restriction hysteria.