Amplifier current vrs watts; why is current more important?

Your typical amplifier outputs volts.

not quite right. Voltage (more correctly known as EMF, electro motive force) is the force that pushes energy out of the amp, down the cable, and into the speaker. Therefore, saying that an amp "outputs" volts is incorrect. I know it is confusing because you often see the term "output voltage", but that means the EMF measured at the output terminals, not that it is putting out volts.

Most amplifiers today are designed to act as much as possible like perfect voltage sources i.e. no matter how much energy you try to get out of the amp the voltage will remain constant. This is of course impossible, but what the original OP is referring to is how well a particular amp achieves this goal. There are also amplifiers designed to act as much as possible like perfect current sources including some of the offerings by Pass at First Watt

If an amp can maintain its voltage as the impedance drops then it has to deliver more current to do so. The better it is at doing this the "stiffer" it is. Conventional wisdom is that the stiffer an amp, all else being equal, the better it is. Of course, nothing is ever equal so whether or not this correlates to better performance is debatable and very dependent on the load the speaker presents to the amp.

Two power amplifiers that have the same power supply voltage may not have the same output current.

also not quite right. If 2 amps have identical output voltage into the same load they will have identical output current. It should say that 2 amps with the same power supply voltage may not be able to deliver the same amount of current. I know I am being picky but the lack of succinctness is what causes a lot of confusion among those with a limited knowledge of electronics. Amps do not output volts, they output current. Amps do not "have current", they output current.

Massive current gain stages are usually less linear than more modest stages and require more feedback to keep behaved

this is also incorrect. Typically an amp consists of a voltage amplifier or stages of voltage amplification followed by current gain from the final stage. This current stage is usually some variation on an emitter follower which is extremely linear. It is the previous voltage stages which tend to be non-linear where negative feedback is often employed to make them more linear. It is not unusual to have an amp with less unloaded voltage gain that is capable of delivering a lot more current into a low impedance load than one with a much higher unloaded voltage gain.

'High current' is a marketing thing. As others have pointed out, you don't need that much current to drive high power into low impedances.
If you are looking closely and doing the math, it becomes apparent that the current 'rating' of many solid state amps isn't real. Here's more on that topic:http://www.atma-sphere.com/Resources/Common_Amplifier_Myths.php
Because those high current ratings you often see aren't about the output of the amp, there are tube amps with similar current ratings, such as our own MA-2, which has a 'current rating' of about 50 amps.

Your typical amplifier outputs volts

It may be a bit oversimplification.  Two power amplifiers that have the same power supply voltage may not have the same output current.  Ultimately it's neither the voltage or current, but the overall design that determines the quality of the sound.

You may have a massive 800W power amplifier with massive output current but it may not provide quality music reproduction compared to a more modest 250W amp.

Current is only of import when speakers dip to low impedance or have challenging phase angles, or both. Otherwise it is of little consequence.

There are so many wrong's in this statement.

Also a read from Pass Labs First Watt will help.  

Because amplifiers don’t deliver watts. (How many watts of light does a lamp deliver? Depends on the bulb, i.e., the load).

What they mean is that amplifier wattage is rated at load of 8 ohms and any change in that load will demand more current from the amplifier.

Example:

100 watts into 8 ohms ---> Voltage is 28V, current is 3.5 amps, transformer 100 VA (~watts)

When the speaker dips to 4 ohms, the voltage can only remain constant if the power supply can deliver 7 amps. To do this, the transformer has to be at least 200 VA. Twice as big.

At 2 ohm load, the PS has to supply 14 amps to maintain voltage, meaning the transformer has to be 400 VA minimum.

If the voltage cannot remain constant -- the transformer/filter caps too small -- then the amp has a hard time driving the speaker through its varying load. This is an oversimplification but by Ohm’s law shows why current is dependent on the power supply and not the nameplate rating.

Andy, are you addressing the Q of the OP or changing the topic?

I think the OP wants to know why current is more important than "watt", but I think what he really wants to ask is why two amplifiers may have the same "wattage" rating but one amp may appear to have more "power" than the other.  He is thinking maybe because one amp has more current therefore more power.  It is only partly true.

My response was meant to say the "current" itself may actually not it, but a better characterization of how "dynamic" the amp is by using slew rate measurement.  

So in that sense, I was responding to his "inquiry" but may be in a different way. 

Andy, are you addressing the Q of the OP or changing the topic? You say that both wattage and current are both static variables. How have you advanced his understanding about his Q?

As an analogy using cars, watt is like a car speed, whereas slew rate is car acceleration.  

Let's say you have two car: a good old American muscle car and a Ferrari.  Both cars may be able to do 150mph, but the Ferrari will accelerate to 150mph much faster than the muscle car which is what most people want.

The late Charles Hansen used to say that an amplifier is basically a power supply design in which the supply is being modulated by an external musical signal.  

Wattage measurement is a static number that has no "time" variable, but in music, timing is everything.  Current is also a static variable without "time".  For example, if you say I want 7Watts but it could mean it will take 2 secs or 10 secs to get 7 watts.  In an orchestra crescendo, you need 7 watts right away.  A good amp will supply that 7 watts almost instantaneously whereas an inferior amp will not, therefore reducing the impact of the music.

A better metric for measuring an amp transient response is called "slew rate", that is how fast it responses to a change in input.

For any given amp, the slew rate will respond proportionally to the load (impedance) of the speaker.  That is the higher the load (higher impedance), the faster the slew rate.  That is why speakers with low impedance, you need higher power amp so that the slew rate will be adequate otherwise the music won't have any dynamic.  

It's not more important. Power, Voltage, Current and Impedance are all related.

P=I^2*Z = V^2/Z

So depending on the impedance of your speakers I or V could be the limiting factor.