"Watts" Versus "Current"

Watts = Current * Voltage

Watts = Power = W
Current = Amps = A (current is similar to water flow)
Voltage = Volts = V (voltage is similar to water pressure)

So you can see that both current and voltage are important in making up a power/watts rating. A good example you may be familiar with is tube vs solid state amps. Tubes are voltage driven devices. They operate at low current but high voltage and control/amplify it easily. Transistors operate at low voltages but control/amplify current easily. So you can see that to get 1W you can have 1000V * .001A or .1A * 10V

As Mapman says, which is better depends on your speakers. Everything above is in general, and in general, woofers sound better with lots of current. So SS is generally considered a better choice over a tube amp with a similar rating. Tweeters don't use much current so they tend to sound better with tube amps. And yes, midranges are in the middle so it's your choice.

Now marketers say just about anything and everything so you just have to take all that with a grain of salt. It's really not which is better (wattage based on high voltage or high current), it's which sounds better in your system to you.

One last analogy that helps understand voltage vs current is that of water pressure (voltage) and flow (current). Think of a great big water reservoir up on top of a mountain and you're at the base of the mountain (yes, this is your power supply :).

Let's say you want to design the system to put out a forest fire should it get near your house. To do that you need a lot of water flow really fast. So you make sure to connect a really big pipe down to your house. Now you've got a system with high water flow (current) that will flow for a shorter time but put out a raging fire.

Conversely, let's say you need to shoot a small stream of water over a large ravine next to your house. Now you can run a smaller pipe to build up the water pressure/voltage. The water at the end of the pipe will shoot out of the pipe, over the ravine and save the endangered species from drought.

Both systems are doing work but with vastly different design parameters required for flow/current and pressure/voltage. Which is better? Well, it obviously depends on what you want to do with the water :)

As many have pointed out, this ignores resistance, impedance, capacitance, or any other kind of system feedback/overload that can impact the system. But I hope it helps to get the general idea across very simply.