There are a lot of variables to worry about. Is the entire top screen? 4x2x what? What materials is it made from? Either way, I would opt for RHP > CHE for a BP because of drying, and having a screen top will only increase the issues from CHE. It may be worth covering part of the screen with plexiglass to keep heat and moisture from escaping so rapidly.
I haven't done bioactive for a BP, but having done bioactive, I think it can work just fine if it's planned properly. You need to pick appropriate plants, have deep enough substrate, and allow the plants to really get a good root structure going for 6-8 weeks before introducing the BP. Putting the animal in freshly after planting plants, they are going to get ripped out in a hurry.