Not the correct answer
The question that Midcow2 asked was not answered correctly.
If amplifier X is rated at 100 wpc and amplifier Y rated at 200 wpc, then assuming that these ratings are both based on the same distortion level, amplifier Y will deliver twice as much power to the speakers than will amplifier X, at that specified level of distortion, regardless of the class of each amp or its efficiency.
The difference in efficiency will reflect in the amount of power consumed relative to the amount delivered to the speakers (and relative to the amount dissipated internally). In an amplifier that is 90% efficient, 90 out of every 100 Watts consumed will be delivered to the speaker. The total power consumed is 100/90 = 1.11 times greater than the amount delivered to the speaker. To deliver 100 Watts to the speaker, 111 Watts will be consumed in total (.9 x 111 = 100). In an amplifier that is 50% efficient, 200 Watts will need to be consumed in order to deliver 100 Watts to the speaker.
When the 200 Watt, less efficient amp is consuming 200 Watts and delivering 100 Watts to the speaker, and the 100 Watt, more efficient amp is consuming only 111 Watts and is likewise delivering 100 Watts to the speaker, amplifier distortion will not be the same for the two amps, because per the distortion ratings that were given in the question, the 200 Watt amp will be able to deliver twice that much power to the speaker before it exhibits that same standard level of distortion that the 100 Watt amp does when it is delivering 100 Watts to the speaker.
Note also that wheres it may seem that the amp with the 200 Watt rating is twice as good as the amp with the 100 Watt rating, "twice as good" is not a substantive concept. The difference is 3.01 dB. The oft-heard notion of "twice as loud" is similarly not well-defined. Who is to say that when one sound seems "twice as loud" to one person, that it will also seem "twice as loud" to another person? It typically takes at least a .5 dB change in volume before most people would detect any difference at all. Modern amplifiers and receivers that use digital volume controls typically change the volume in steps of .5 dB, and when you observe on the display that the change is exactly .5 dB, you can barely tell that the volume has changed at all. The bottom line is that a 200 Watt amplifier is stronger than a 100 Watt amplifier by a modestly useful amount. If you want to get a better sense of the difference, find a modern digital receiver and turn up the volume about as loud as you can stand it, then turn it up some more until the display indicates that the volume has increased by 3 dB. That difference is the difference between a 100 Watt amp and a 200 Watt amp.
Note, finally, that the vast majority of the power that is actually delivered to the speaker is dissipated as heat in the voice coil (and also in the crossover). Speakers require gobs of power from the amp because they are horribly inefficient, way less efficient even than most any amplifier. And the difference in speaker efficiency varies considerably from one speaker to the next. As a general rule, there is a trade off between the sound quality of a speaker and its efficiency. Speakers that sound exceptionally good will often be more than 3 dB less efficient than typical speakers. Often the difference will be 5 dB or more. The difference in speaker efficiency can easily overcome the difference in amplifier efficiency. If you connect the 200 Watt amp to a speaker that is 3 dB less efficient than the speaker to which the 100 Watt amp is connected, then both amplifiers will hit the ceiling at the same actual volume that you hear, i.e., SPL.
Expensive amplifiers are generally a waste of money. As long as they are not driven into clipping, amplifier distortion is typically one or two orders of magnitude less than the distortion in the speaker. Non-linear distortion is routinely quoted for amplifiers, but never quoted for speakers, and rarely measured in reviews. This is all a throw back to the old vacuum tube days. If you like your music at deafening levels, then it can be important to pay attention to speaker efficiency, since you could end up needing a more powerful amplifier, the incremental cost for which will likely be greater than it ought to be. The best buys in standalone amplifiers are found at the musician stores, but they often don't come with the desired form factor and cosmetics, and they often don't have the right sort of inputs and outputs, and they don't come in the package that we know as the A/V receiver. But if you are just looking for a high power stereo amplifier and don't care about the aesthetics, the musician's store is your friend. Most people in most home environments who listen to music as opposed to car crashes and explosions of various sorts do not need to be concerned about the efficiency of the speaker, because most any modern amplifier of ordinary quality will drive even the most inefficient modern speaker to very high volume levels without the slightest amount of strain.
