We raised 60 heritage turkeys and were very frustrated in our efforts to contain them. They flew over the fence with ease and preferred roosting in the trees rather than any structure we made. We lost over 20 birds to cototes and were forced to clipping a wing on each bird in an effort to keep them contained. This didn't work for all of them, but if only 1 got out, it would spend the rest of the day walking around the fence trying to get back in.
Did I mention it was frustrating ; )
You would probably be fine with a broad breasted variety, but I have no personal
experience with them.