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.