The two concepts are neither the same nor mutually exclusive. Neither is inherently "right" at the exclusion of the other. They both work toward the same goal: to reduce microvibrations that affect sensitive electronics and distort the music. Both concepts can be engineered into equally effective products. (Turntables are also particularly susceptible to macro-vibrations, such as footfall on a suspended floor; neither high-mass damping nor draining alone will alleviate these vibrations.)
High-mass materials don't necessarily absorb microvibrations due simply to being high-mass. Mass and density help to control vibrations as much by confining vibrations as by absorbing them. Generally, the harder a material is, the more readily it will transmit vibrations instead of absorbing them. This lends these materials to attempts to "drain" vibrations away.
Unfortunately, draining vibrations doesn't always work as well in practice as in theory. There is no "traffic cop" to direct vibrations to the drain. Microvibrations are more like ants at a picnic, traveling in every which direction, especially through and between hard materials. Some vibrations are drained, but to where? To the rack, where they will reciprocate back to the component re-armed with sonic character from the rack and infiltrate other components. Or to the floor, where they will reciprocate back into the rack and across to the speakers. Hard materials, brass, even the hardest metals and ceramics, virtually all have unique sonic signatures that they introduce into the vibrational environment. Rigidly coupled systems, whether high-mass or low-mass, usually have a lot of detail, but tend to be harsh. To reduce coloration and bring out more ambient detail, it's usually best to have some compliance to break up the flow of microvibrations through rigid materials.
Softer materials can absorb and block micro and macro-vibrations. Most compliant materials like rubber and Sorbothane, however, have resonances that cause bloopy bass and muddy sound. It's a trade-off: some vibrations are reduced while others are introduced. Materials with very low resonant frequencies are usually too "slow" to provide the counter-vibrational response necessary to absorb acute higher frequency vibrations that cause so much glare and harshness. To best achieve the kind of vibration control necessary for audio equipment, you need materials that are formulated specifically for the vibrational environments that are peculiar to audio systems.
It's usually not possible to "overdamp" strictly by reducing vibrations. When the damping material itself has any sonic or resonant character, though, or when it simply alters the vibrational environment, overdamping happens readily. "Overdamping" also occurs when symbiotic relationships between parts are altered. For example, let's say microvibrations cause a CD player to emphasize higher frequencies and this is "corrected" by attenuating higher frequencies at the speakers. If the vibrations that cause the emphasis in the first place are then reduced, allowing the CD player to provide a true and linear result, the attenuation at the loudspeakers would then overcompensate, resulting in what might be perceived as "overdamping" of the CD player.
If done properly, damping a tonearm is beneficial because it reduces unwanted vibration. The tonearm does not carry information by vibrating. A tonearm functions best when holding the cartridge as vibration-free as possible, allowing the stylus to accurately trace the record groove and vibrate only according to the information cut into the vinyl--not by intrusive vibrations. (When damping a tonearm, you'll adjust the counter-weight so the stylus pressure and arm pivot keep the same sensitivity.)
With damping and isolation in general there is no "right" or "wrong" approach. You need both. Some parts you want rigid and/or dense; with others, you want some compliance and "give."
For more insight into related topics, there is a thread further down on this Circle called, "coupling vs. isolation" and an overview of Herbie's compliant footers here:
Footers FAQ Best regards,
Steve Herbelin
Herbie's Audio Lab