Amplifier current vrs watts; why is current more important?

With digital room control you can do whatever you want as long as you have enough power, volts and current to support the corrections. Power is everything in a SOTA system. The problem with low power high efficiency solutions is that power requirements are geometric. They go up dramatically with peaks. Low power systems can't support this unless you just listen to string quartets. The other problem, and this is my ears talking, is that horns always sound like PA systems to me.
An amplifier is a voltage source. It's job is to pump electrons stored in the power supply into the speaker. If the speaker is high impedance fewer electrons (current) are required to do the job. Lower impedance than more electrons. If the power supply runs out of electrons all the pumping power (voltage) in the world will not do any good. None of this says anything about efficiency.  

In a simple DC circuit, Amps = Volts/Resistance. Watts = Volts X AmpsUsing the water analogy, Voltage is the pressure pushing the water thru the pipe, Amperes,(current) is the volume of water & Resistance is the size of the pipe restricting flow. When you introduce AC current with coils, capacitors & such things get much more mathematically complicated, as the previous posts outline. Thank Heaven for the brilliant engineers who design our great gear.

As a Magnepan owner I will tell you I went through a couple amps trying to get the best out of them.  Maggie's are notorious for chewing up lesser quality amps and spitting them out.  They literally put one amp of high wattage into protection mode within 5 minutes and cooked the power supply.  I had a couple of monos built with about 220 watts but monster current and I finally heard all that the Maggie's had to offer.  Too much emphasis on watts.  

George - The " tone control" effect you speak of is due to output impedance of the amp. 
Man so much misinformation on here and the question was simple. The answers are going way off topic. 

I have the so called "easy to drive" Legacy Focus speakers because of their high 98 db efficiency.  But their low impedance (subsequent 20/20s were more difficult to drive) and 4 ohm preference make them difficult to drive.  Maybe it's their 3 12" woofers.  Anyway, an EAR 890 amp has great difficulty in driving them, lacking in bass and dynamics and just sounding pushed.  It's a Class A 70 watt design.  It sounds excellent on the Legacy Signature IIIs which have 3 10" woofers and slightly easier impedance curve.  

I can drive the Focus speakers with a highly modified 35 watt Dynaco 70 which has an electrolytic cap the size of the chassis underneath as opposed to the original.  Lots of power stored in that cap.  They're plenty the Sig. IIIs.  For the Focus speakers, I use a pair of 130 watt tube monoblocks, custom made, with 2 3" X 7" storage caps, huge compared to the tiny row of caps found in the EAR 890.   I  bet my big amps could drive most any speaker despite the limited wattage (although tube watts are 2 to 2.5 times more than SS watts generally, not including  Pass amps or other high current ones).