... how important is Damping factor in determining what amp to buy

Who wouldn’t want better control of the bass drivers? Wouldn’t that yield tight and accurate bass

Actually no. It **might**. Any loudspeaker can be overdamped- IOW, you can have too much damping. The result is 'punchy' bass without much in the way of definition (also called 'body' when low frequencies are being described). The correct bass will have punch and definition at the same time.

If you have too much damping, the speaker can't make the excursion it should to reproduce the waveform- which is why you loose definition. On top of that, the **amount** of 'punch' you get will not be correct (punchy, but not enough). A lower damping factor can allow for more bass excursion. Too much excursion of course and you have muddy bass, but IME that is actually pretty rare- most acoustic suspension speakers are internally damped already, while most bass reflex, horn and open baffle designs (which includes magnetic and electrostatic planars) really don't need that much.

I seriously doubt that 0.45% change is audible. However, a general rule of thumb is that an amp with a DF of 20 or below has sonic consequences. Doing the math, the speaker in this case is 95% of the load -- a considerable change that results in sonic degradation from dynamic load variation since the amplifer is no longer a perfect voltage source .

The 'traditional' thinking here is that frequency response is the last word on tonality.

It isn't.

It turns out that the human ear/brain system assigns a value to distortions; they are translated to tonality. In fact it now appears that there is a tipping point wherein colorations created by distortion can be favored over actual frequency response errors.

In addition, the use of global negative feedback is well-known to contribute to higher ordered harmonics (see Norman Crowhurst). The higher ordered harmonics are used by the ear/brain system to detect volume levels (rather than the fundamental tones). The result of trace amounts of higher ordered harmonics is called brightness and harshness because of human sensitivity to these harmonics.

This is why many designers don't use feedback and frequently favor tubes- to avoid that particularly annoying coloration. This often results in a high output impedance/low damping factor but this can be easily dealt with giving careful speaker selection. 

@mapman, if I recall, your speakers are 4 ohms. Damping factor as a spec is usually stated with respect to 8 ohms. So in reality your speakers seem to need an amp with a damping factor of about 25, once you correct for the impedance. As I stated elsewhere, no speaker needs a damping factor of more than about 20:1 or so; your speakers seem to be within that ballpark.

Here's a further link:
http://www.dissident-audio.com/Loudspeakers/CriticalLSDamping.pdf

If the speakers are not broken in, they are most likely to be over-damped.