Badaling or Mutianyu in March?

Planning to around March 17. I’ve read that Badaling is the more popular one and therefore more crowded. I wonder at this point in mid-March, which one would you recommend? We’re aware of the weather and will dress accordingly

Also I will try to buy tickets for the Forbidden city a week before when the ticket sale open, does anyone know at what time exactly the tickets are released? They go out so quickly so trying to maximise the chance to buy it