Even though the OP’s title is
"Amplifier current vs watts; why is current more important?"
Just to take it off topic as
oddio did, with his (excuse me) even grosser misinformation.
To show why output impedance (damping factor) is not the only cause for "tone control" behaviour, but also "available current" is just as if not more important.
Here is a typical case where "current" ability is the factor to making a flatter frequency response, more so than output impedance (damping factor)
Here are two very similar (save for their current ability) amps solid state linear each 60w into 8ohms, but their output impedance (damping factor) is more that 10 x different from each other, these are frequency response measurements (black trace) into exactly the same Kantor simulated speaker loads.
NB: Make sure you see what the graph graduation scale is for both.
1: This Budget Schiit is the one with lowish current , but the "best" lowest output impedance ( best highest Damping Factor) of DF=226 Output impedance=0.03ohm It’s FR is +- 2db
https://www.stereophile.com/images/416Schiitfig01.jpg2: This Pass Labs one with high current but, worse 10 x higher output impedance and worse 10 x lower damping factor especially in the bass, and yet has far better control over the same simulated speaker load. It’s FR is only +- 0.025db!!!!
https://www.stereophile.com/images/1116Pint60fig01.jpgAs you can see the one, 1: with the "best" lowest output impedance (highest damping factor) is the one behaving like a "tone control" more that the other!!!!!!.
This is because the Schiit is current is limited into the low impedance loads of the simulated Kantor speaker load compared to the Pass labs.
Now back on topic, sorry
hiendmmoe Cheers George