I think you'll find that the primary damping effect in a Helmholtz tuner is due to skin friction on the high speed slug in the throat of the device, and that the phase effects are secondary. This may just apply to air/hot gas systems, not liquid.
A quarter wave tuner uses the phase effect as its primary method of attenuation, as such its bandwidth is less controllable, and generally narrower.
Cheers
Greg Locock