This does depend on your situation. Alone in the woods, I would keep the gun capped and at half cock with the muzzle down. Always be aware of where the hammer is and recheck it often. No mechanical safety should ever be relied on. Your awareness and muzzle-discipline is the only safety that you should rely on. Carry the rifle so that if it were to fire at any time there would be nothing in the path of the projectile that you don't want to shoot.
At the range don't cap the gun until you are at the firing line with the muzzle pointed downrange.
At the range don't cap the gun until you are at the firing line with the muzzle pointed downrange.