current versus watts

Dangelod:
with the best amps doubling output as impedance is is halved.

you're talking audio, man! what's 'best' for you could be 'trash' for another listener! There's no objective definition of 'best amp' in this hobby - it's all VERY subjective.
So, I'd say that many of the large chassis (think Rowland Model 8, 9, the MBL 1200W/ch used to drive their radial speaker, Gryphon & others in that chassis size) & expensive amps (think top-of-the-line Krells from the late 1980s, present MBLs, Boulder, Rowland Model 8, 9, Gryphon) show this tendency. Most amps in the market do not have this proprty - it's very expensive to make them have this property!!

Dangelod
Seems like all high quality amps clearly describe output in watts........
But, I do not see(often) specs on current ?

That's because Power = Volts * Current = Current squared * Impedance (or Resistance). So, if you know Watts & Resistance you can calcuate the output current. Herman has already done those calculations for you in an earlier post. Those calculations pertain to maximum output DC current of your hypothetical 300W/ch into 8 Ohms i.e. output current when the amp is outputting 300W. You should realize that such an event is unlikely to occur frequently unless you are listening to music at paint peeling high levels (& ruining your ears!).

Dangelod:
Is high current as important to quality dynamic sound as high watts.....
If so, what are the general ranges of current output that would be acceptable for a high quality amp.

yes & no - depends on the speaker you are using. Some speakers are notorious for needing a large reserve of current to drive them to their best performance & other speakers are an easier load on the amp. Hence, there is no clear definition on what is considered a general range of output current. As another member pointed out - depends on the speaker impedance-phase curve.
But, as Atmasphere wrote before, whether you output small amounts of current or large, you need to do so with minimal distortion otherwise the sonics are strident. At high distortion levels it won't matter whether you have the "best" amp or not, the music experience will come up way short.

The conclusion is that the amplifier-speaker interface is a complex one because the speaker load affects the amplifier output impedance & vice-versa. Plus, the speaker impedance & phase varies over frequency. So, as you run up/down the audio spectrum, nothing remains constant! So, you will not be able to take a fixed number (amplifier output current as you are asking) & apply it to an interface that has variable performance....
IMHO. FWIW.