I'm a huge fan of shooting sports and couldn't agree more that they are an excellent platform for growing character in young people, but I don't know that they are "superior" to other outdoor activities that can be done between fathers and children. As a father of three, I find that the magic isn't so much the shooting but the environment. In the woods we are free from electronic distractions and other societal temptations. We can slow down and be still. Even when we're not "shooting," my sons and I have had amazing times camping, canoeing, hiking, fishing, etc.
Of course, the most significant issue is the willingness of the father to prioritize those times and experiences and invest in their children. Any dad who is willing to do that will be well on his way to developing a higher functioning adult.