Hat still firmly in place: For a given speaker, power does equate to loudness. A speaker's efficiency is measured in dB per watt.
That dB/W rating varies from speaker to speaker of course, so 10W through an efficient speaker can be as loud as 100 through a subwoofer with a heavy cone.
To be clear, I'm talking about the watts the amp delivers into the speaker, not the amount of power it draws from the mains. A mosfet based class AB Trace, for example, is a lot less efficient than a modern class D so the power rating on the IEC inlet isn't an indication of its ability to be loud.