It looks like "Lid On" is the winner by a huge margin. What made me ask is the fact that some of the best steaks and burgers that I have ever eaten, were cooked over an open pit. The biggest difference that I have noticed, is that a burger or steak cooked with the lid on always seems to have more juice inside. Kind of like it doesn't suffer from as much evaporation or something like that.
My grandfather always cooked on a open topped grill, and he grilled a steak by just seasoning with garlic salt and black pepper. he put a pat of butter on the top side and turned the steal after 6 minutes, then putting a pat of butter on the flip and cooking for another 6 minutes. Perhaps it is just that "childhood memory" thing, but those were some pretty dang good steaks that he cooked.
Thanks to everyone for answering, it is great to see that everyone doesn't just do everything exactly the same way. More than one way to skin that cat.