The barrel tuner is primarily used for track shooting, where it makes it possible to tune the swing of the barrel. The running tuner extends a muffler by approx. 30 mm, and increases the sound attenuation. You can advantageously take a module of the damper, then the extension is only 10 mm, without loss of damping.
The barrel tuner adds about 100 grams of extra weight. This is typically an advantage when shooting range, but again a reason why running tuners do not find widespread use in ordinary hunting situations.