Damping Factor

Basically all high damping factor (DF) tells is that the amplifier has very similar voltage output into an 8 ohms resistive load and into a a no-load (aka infinite resistance load).

There are loads of conjectures on how a very high DF affects sound quality, but such conjectures are severely restricted to closely identical topology and loudspeaker loads. For example, when a specific solid state circuitry's DF is 20, and it's improved to with minimal alterations to its topology to 200, there is a noticeable improvement in bass performance when driving low efficiency, current hungry loudspeakers. The applicability of DF-centric paradigm / observations are restricted to this playing field. The actual DF count means something very different for a class D amplifier than a class A single ended amplifier, the numbers are not comparable, as their voltage / current generation and handling mechanisms are very different.

In general, DF is provided for an 8R purely resistive load at 1kHz frequency. (Unless otherwise specified.)

However, to make DF useful, (whether it helps you or not), you need to know what the DF is in the actual region where it has significance: the 20Hz-100Hz region.

A DF of 1000 at 1kHz is useless when the DF at 20Hz is only 20. (However, it is unlikely to have super low DF at 20Hz when DF at 1kHz is very high, but it's not guaranteed.)

Even worse, the DF has to be recalculated for YOUR LOUDSPEAKER to tell how your amplifier is handling the Loudspeaker. How it handles a nominal resistor is fundamentally different from how it handles a loudspeaker.

My experience:

-Solid state amplifiers are kings to handle resistors, but they don't do so well with loudspeakers.

-Tube amps do not do so well with resistors, but do much better with loudspeakers, provided that loudspeakers are a match to them. (Neglect impedance matching = failure.)

DF in the marketing literature: we are measuring a phenomenon at the wrong frequency and with the wrong type of device. 1kHz instead of 20Hz, and with 8R resistor instead of an actual inductive loudspeaker. This is like measuring a swimmers performance doing squats in the locker room, instead of actually clocking his swimming....

Coming back to applicability: high DF counts when driving low efficiency & current hungry speakers, which need tremendous control over the cone, as the energy required to reach the same spl can be x100 or greater than with a high efficiency speaker.

Briefly: if you can see the cone move, you need high DF. If the cone does not move, DF is almost irrelevant.

Agreed, if the cone doesn't move much then DF is not as important. It's all about control of the diaphragm. Some people like loose and some like tight, I'm in the tight Fanclub.

Speaker designs changed when solid state amps became popular and power was no longer a big concern. Smaller enclosures, lower efficiency and much higher Xmax in the LF drivers. All of a sudden cones were moving a lot. Stopping them from moving was done mechanically, or electrically. Mechanically by surround and spider, electrically by the motor. If you are using a high efficiency large driver, with a low xmax, DF not such a big deal. But, if using a small driver, with a high xmax that is low efficiency, then you want high DF. The speaker has to be controlled and made to stop when there is no signal. 
 

Like most things in audio, it depends.

Ok so tight equals high DF, punchy bass? Best control over a woofer cone? And maybe that is why class D amps sound as they do? I'm curious.

If deep and tight bass were the be-all and end-all of amplifier performance, then only solid state amps would be in the market (cheap ones can deliver this).  But, there is so much more to performance, even in the bass range.  I have no idea if tube amps that are not as tight sounding are coloring the sound and  adding in distortion, I only know that I like the upper bass performance of many lower-powered tube amps -- bass has a better sense of subtle and varying "tone," it has less of a dry quality and "mechanical" sameness.  I hear the same sort of dry and toneless bass with many high-powered tube amps, so it is not necessarily a solid state vs. tube issue.  The amps I tend to like probably have a low damping factor, but whether this is the "cause" of the sound I like or whether it is just something that attends the basic designs that I like, I don't know and don't really care.

In short, I don't think damping factor means much at all, and it certainly isn't a high priority consideration, beyond some minimum that affects basic compatibility with a given pair of speakers.  I would not worry about damping factor at all if I had genuine 16 ohm speakers.  With an 8 ohm speaker, I might be concerned with an amp with a damping factor below 8 (but I would still audition because there is a good chance the combination will still work out).  With 4 ohm speakers, i might be a little concerned with something below 15.  I've heard SET amps with 4 ohm speaker that sounded terrific, and many of these don't have have damping factors above 4.