I have only been to Brookeville a few times but have always gone when they first open. You might have trouble finding a spot for parking and a table for that many people in the afternoon.
Look at Loan Oak. They have a lot more parking, and it might look crowded when you arrive but they have a huge open outdoor space (field) versus Brookebille. At Loan Oak, they have picnic tables, but if you don't get a picnic table, there are many grassy areas where you can put a picnic blanket and chairs.
You can always drive by both places before making a decision around the time you are planning to go. They are close to each other. Obviously, it depends on the day regarding how crowded it is, but it might give you a better idea of which one you want to pick.