If you can help it, you should avoid scheduling back-to-back closings. The reason for this is that closing delays are often unavoidable. If you do not allow plenty of time between the closing of the sale of your home and the purchase of your new home, if the first closing delays, it will impact the time of your second closing. You also need enough time to physically move from one location to another, if the same closing attorney is not handling both transactions.
If you must schedule both closings on the same day, your best bet is to schedule one in the morning and one that afternoon.