Any bow hunting is hard; private land, public land, small game, big game, there is no such thing as an easy bow hunt. That is part of the beauty and appeal with bowhunting. The only thing different about public land compared to private is the amount of pressure.
The deer don’t know the difference in public or private they just know when and where they are pressured, and adapt accordingly. With that being said, pressured deer are tougher to hunt and may require different tactics to be successful; things, like hunting during the week, hunting midday, and hunting on bad weather days, can all improve success on pressured deer.