<< Having a nice Denon or Harmon amp that is rated at like 60 Watts a channel is much nicer then a SONY that is rated at like 120 or more per channel. >>
That's total bullsh!t. The FTC requires (for home audio, NOT cheap computer speakers) power ratings to be "RMS" and other measurement parameters to be stated. "Peak power" ratings are never seen in home audio gear. And they are meaningless for cheap gear.
Some manufacturers are more conservative in their ratings, as there is no law that says you have to test in one specific way. So, one manufacturer's 100W per channel amp may deliver a max output power of say 103.7W when tested a certain way, another company's 100W per channel amp might deliver say 119.3W when tested the exact same way. It's not like one company is lying and the other is telling the truth, though.
A typical power rating might look like "100W per channel into 8 ohms, 0.01% THD, 20-20,000Hz, all channels driven" or "100W into 8 ohms, 0.01% THD, 1 kHz, one channel driven" The difference between the two ratings is that the first one means the amp can deliver 100W at any frequency between 20Hz and 20,000Hz, while any other channels are also delivering 100W at any frequency. The second one is a much narrower (although still valid) measurement. The catch is that this spec means power output could be significantly lower if 2 or more channels are reproducing any sound at the same time, or if the frequency of the reproduced sound is different than 1kHz.
The key variables are:
distortion, THD in % - distortion usually rises drastically as power output limits are reached. 0.1% is completely inaudible distortion. Most high quality speakers have THD over 1%, and more than 10% for low bass frequencies
impedance, in ohms - power output is higher into lower impedance
frequency range, in Hz - it is more difficult to deliver power across a wide frequency range than across a narrow one.
time - RMS (current and voltage, not power directly, as jamarno correctly pointed out - but power=current X voltage) is measured over an extended time period. Many amps can deliver very brief (i.e., microsecond) peaks in excess of 1,000W. But after the filter capacitors for the power supply are drained, power output will be the stated RMS value.
Probably more than you wanted to know.......