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

well well well,,,,,,,first of all,,, things have to be clarified here,,,,,1e taste is unique for every one ,,, so what can describe as tight bass for one could be muddy for another ,,, just like colors ,,,, smell ,,,,, etc etc
2e damping factor is highly degraded by speaker wire caliber and lenght ,,, for low inpedance amplifier ,,,,3e higher outpout impedance amp ( lower damping factor amps ) are less prone to that

now lets talk damping
my set up is the following
 i have 2 proel double 15 inches subs rated at 800 watts each 4 ohms
i drive theses with one k2 crown for each
my speaker wire is 15 feet long  10awg
the k2 damping is rated at 3000 at 8 ohmsso using a damping factor calculator  i made some test and came up with these numberswith the regular setup sated earlier  i had 127 df  because of the 4 ohms
i opened up the subs and made separate connection to each drive ( 8 ohms )  df when up to 150  approxdid not ear much difference , then i hook up the subs in series bringing the df to 453 approx
oh boy now i did get a noticeable difference in sound clarity and punch
witch drive me to change my next set up ,,
i will bring the k2 on the side of the subs  and use 6awg  of about 4 or 5 ft  passing trhue the port hole to connect the drivesaccording to the df calculator  this should bring me above 1400 df  of real damping
after this test ill be in a real position to tell if the sound difference is really different from 453 to above 1000if it is the case the next step will be  drilling the side of the subs , installing news wire terminals foe 2/0 awg wire  (00)awg
then with the shortest length of wire possible ( around 3 ft max in and out ) this shall bring me at around 2700 of damping  out of the 3000 rated by crown ..but i can already testify that just by changing the speaker impedance/ wire size and lenght , that sound did change a lot ,,,
so the real story about damping is this
unless your power amp is extremely close to the speaker , and the wire size is extremely large , you cannot benefit from the high damping factor rating from your amps
 the higher the damping rating is , the lower the amp output impedance is ,, and this is extremely sensible to the speaker wire impedance,

amps with lower damping are less prone to this therefore the tend to lose less of there df rating .
here is a good post about it
http://www.bcae1.com/dampfact.htm
remember ,,,, speaker wire should always be the largest you can physically  install or afford.
speaking of damping factor is futile if you run 18,16,14,12 awg  wire

When a signal is sent to a speaker to play a note, the cone vibrates. When the signal stops, the cone is still moving back and forth. and is an electric motor. This movement sends the electrical signal back to the amp, and a highly damped amp will stop the cone sooner.

Amp won't make much difference in damping, since there are already many ohms of the speaker's voice coil in series.  Overall effective damping factor is around df=1.5 at best.  

Oh god... Another big guage nut. 

With a link to a car audio page no less...

I don't understand this philosophy of looking at the cables as some weird extension of the amplifier when they're most definitely a reactive load unto themselves. The car stereo article really doesn't tell the full story because it's mostly concerned with driving the subs in the trunk of some kid's 2003 Honda Civic. 

Cables have inductance, resistance, and capacitance and they can be modeled by a resistor, inductor, and capacitor wired in series. It should be pretty obvious that the behavior of such an arrangement is going to be extremely dependent on the frequency of the signal. The impedance and damping characteristics are going to depend entirely on the frequency. 

It would be really nice if cable manufacturers provided real numbers on what their cables measured like because they have to know what they are to design the things like they do. Looking at real measurements it becomes obvious that proper cables can compliment and focus the damping characteristics of the amplifier, and wrong ones can work against achieving the best results. And no, just throwing jumper cables at the problem isn't a solution. If it were, everybody would have 4g cables. 


https://www.passdiy.com/project/articles/speaker-cables

Three plus years ago I was "on a mission" to find a new pair of floor-standing speakers.

One of my stops was at a dealer to audition the then Magico S5's.  As the "main" listening room was occupied, the salesman hooked the speakers to a Hegel power amp with a very high damping factor.  When the "main" listening room became available, he wheeled the S5's over there and connected it to a pair of large tube monoblocks, with a very low damping factor, and driven by tubes, the Magico's sounded much more "musical" and had more bass.  I suspect that, the pairing of a low damping factor and the Magico bass driver just worked better together.