I hunt with a slung revolver - a 7.5" and 9" 454 FA.  This is my preferred way to carry a big gun.  For a few reasons, but the primary one is experience.  When I hunt, I carry a daypack, and binoculars on a bino-buddy rig, and a rangefinder.  The most comfortable way to carry a holstered scoped revolver is the FA chest rig, in my experience, or some other shoulder holster, which is just one more set of straps running around my torso.  With a sling, I wind up much more comfortable and flexible and the gun is just as fast to get into action.  I don't shoot with a neck sling - never have tried that - but some advice from those who do is to adjust the sling so that it is useful as a neck sling, and then put another set of clips on it to that it will take up in length to be useful as a carrying sling.
Mine is a 1" leather strap that I had Rob at Simply Rugged make, 36" long.
And just for the purists that think this is a sin, I always carry a belt gun as well.