current versus watts

Seems like all high quality amps clearly describe output in watts , with the best amps doubling output as impedance is is halved. But, I do not see(often) specs on current ? why is this ? 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. For example, if you have a 300 watt/channel amp that doubles from 8 to 4 ohm, what would be strong current output ?

Apologize for the simple question and feel free to direct me to earlier post that might deal with this issue