"Green fields", as you refer to them, are usually going to see a lot more deer activity than a natural clearing in the forest, due to a more consistent availability of preferred forage. Depending on the amount of hunting pressure your area experiences, you will probably see more quality bucks in the heavy cover. Specifically, I look for locations just downwind of major deer bedding areas, and then try to find the travel corridor from that location to the green fields most deer seem to be using, at that time. Scrapes and rub lines will tell you if you've found the right starting point.
So, to answer your question, if you want to shoot lots of deer, stick with the green fields. If you'd like to see fewer deer, but a chance at a really good buck, you gotta hunt the thick stuff and not be too frustrated if you hunt all day and don't see anything at all.
It's kinda like, do you wanna catch 50 bluegill, or a big ol' bass? Can't use the same techniques for both, so you have to pick what your goal is and adjust accordingly.