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

Hegel H300 has a DF of 1,000. The new H360 is a DF of 4,000, Hegel advertises this hard in their literature and discussions, seems very important to them and I do love their top integrated units.

Listen to it.....don't even look at specs

From a post by Atmasphere in this thread on damping factor:

There is no speaker made that requires more than 20:1 for a damping factor, and there are speakers that prefer a damping factor of 1:10 (usually high efficiency full-range speakers).

From a post by me in that thread:

Damping factor and amplifier output impedance are inversely related. Damping factor, as usually defined based on an assumed 8 ohm speaker load, equals output impedance divided into 8 ohms. To the extent that the speaker’s impedance varies with frequency, that output impedance will affect tonal balance, by interacting with the speaker’s impedance vs. frequency variation.

Many electrostatic speakers, for instance, have high impedances at low frequencies, which descend to low values at high frequencies. A solid state amp, having a high damping factor and negligibly small output impedance, will produce LESS bass and MORE treble into that kind of speaker, relative to a tube amp. The tube amp, having a relatively low damping factor/high output impedance, will produce MORE bass and LESS treble into that kind of speaker.

Conversely, many dynamic (cone-type) speakers have low impedances in the bass and mid-bass regions, and higher impedances in the upper mid-range and treble. Driving that kind of load, a solid state amp will provide a stronger bass response than a tube amp, and the tube amp may sound excessively bright.

As was stated, synergy with the particular speaker is key.

From a post by Kijanki in this thread on damping factor:

Inductor in-series with the woofer has resistance approx. 0.08 ohm limiting DF to 100.

Adding to the above: Per Atmasphere’s comment, once damping factor gets significantly above 20 or so, further increases will make little if any difference. Although if one amplifier has a damping factor of 50 and another has a damping factor of 2000, it is almost certainly an indication that there are other major differences in the designs of the two amplifiers that will cause them to sound different. Also, once damping factor gets significantly below 20 or so, which is characteristic of most tube amps, and if speaker impedance varies significantly as a function of frequency, differences in damping factor within that range may significantly affect tonality, due to differences in impedance interactions. And, likewise, damping factor differences between those amplifiers and solid state amplifiers having higher damping factors will also result in differences in tonality, to a greater or lesser degree depending on how the impedance of the speaker varies as a function of frequency.

As I said above, synergy with the particular speaker is key.

Regards,
-- Al

... oh man! - was looking for abit more clarity about how important it is in the voicing and control of a speaker; I understand what it is and what it supposedly does and that all amps must have it to some degree... stringreen's approach ( which to me seems to be more financially-based) would have me all over town, listening to not in my space, or with my components...
MOre pointedly: I'm wondering if my vintage Onkyo A7 (65w/c) or Nikko DC Alpha 230 (120w/c) has enough DF to adequately control the woofer in a new-to-me pair of vintage Gershman Avant Garde RX-20s (before 2000) I've got on the way; I've been lead to believe that if a speaker is underpowered that you can damage a woofer, and I assumed this had to do with DF...

It appears that your Onkyo has a damping factor of 50, and the Nikko has a damping factor of 70. Both of those damping factors will be suitable in terms of sonics with any speaker that is suitable for use with a solid state amplifier.

I’ve been lead to believe that if a speaker is underpowered that you can damage a woofer, and I assumed this had to do with DF...

An amplifier that is underpowered relative to the application, and therefore may be frequently driven into clipping, can cause tweeters to be damaged. I am not aware of any means by which an underpowered amplifier can damage a woofer, or of any relation between damping factor and the likelihood of speaker damage.

Regards,
-- Al