Some claim that the slow pressing action, combined with a very fine mesh screen helps to emulsify the coffee oils into the water. Apparently this adds to the fuller flavor and body of a french pressed cup of coffee..... I'm not sure that I believe it or not, I'm just repeating what I have heard from others that are more experienced than I.
True cowboy coffee is different in that it is boiled, or at least simmered over the flame while it is brewing. The French press just gets hot water and is left to sit.
But the biggest difference is that you use your teeth to stain out the grounds as you drink it.