Importance of Damping Factor and Current for amps

I have read that amplifiers with high damping factor and high current delivery can provide deeper and more controlled bass, and also handle difficult speaker impedance loads. Is this true for both solid state and tube amps, whether separates or integrated???
I'm going to find out for sure on Saturday, as I’m going to compare my Coda S12.5 to a pair Pass Aleph monoblocks. The Coda has far more power (125 watts vs. 30) and a very high damping factor, so we’ll see if it controls the bass better on my friend’s Vandy 3As. My other friend, who suggested the shootout, seems to think it will.
This is not a universal truth by any means! If the speaker is over-damped by the amplifier, you will get **less** bass and no definition!

Some speakers want almost no damping and others need some; no known speaker needs over 20:1.

There are two design paradigms for amps and speakers that compete in the high end audio world. You cannot mix equipment from opposite camps as it will result in tonal anomalies- this is the equipment matching issue you hear about so often. For more info see:
High dumping factor, IMO, is useless as I never know will it help or not.

There are some amplifiers with 5000 - 6000 dumping factors which cannot handle difficult load.

On the contrary, high current delivery , is always, always useful and its difficult for me to imagine situation where high current delivery can hurt...

Also, when I say "high current delivery" I mean not over period of a few milliseconds as its only marketing.

Finally, high wattage does not mean that this amp is with high current delivery. Good example is bridged solid state amp e. g. Spectron stereo versus monoblock amp.