The methods used to measure and report output do vary quite a bit from manufacturer to manufacturer. However, I don't really understand what you're asking here. Are you saying that an amplifier that says it's a 1200W amplifier only produces 200W per channel @ 8 ohms? I'll assume this is what you're referring to and I'll explain. The 1200W peak rating would typically be referring to it's bridged configuration at the lowest nominal resistance that it's capable of handling (usually 4 ohms bridged). This is because you're combining the power of both channels of the amplifer and running it through the lowest possible resistance. As resistance goes up, the amount of power the amp can push through the load goes down. So then if you split it across two channels as well, it drops even further. I hope that make sense and explains it for you.
The advantage of a bridged configuration then is that you can combine the power of the two channels in the amplifier to drive a speaker with a higher power handling capacity. So if you need 1000W to drive you sub, you don't need an amp that can deliver 1000W per channel (which is a big and expensive amp). You can use an amp that may only deliver 400W per channel but when bridged delivers 1000W. Now the disadvantage is of course that now you've only got one channel on that amp. So if you need to drive both left and right signals, like for you top-end cabinets, you need two amps.
Matching your amplifier to your speakers is very important as you can imagine. Speakers usually have 3 ratings for power handling. They are RMS, Program and Peak. A good general rule of thumb is that your amplifer should be capable of delivering 100 - 150% of the Program rated (which is usually double the RMS and half the Peak rating) power. Now the other key here is that speakers have different nominal impedance values. As you've seen the amps are rated based on how much power they can deliver at each resistance measurement. So for an example, if I have a pair of 2-way cabinets that have a nominal resistance of 8 ohms and and RMS rating of 350W, I'd be looking for an amplifier that can deliver 700-1000W per channel at 8 ohms.
More power in your amplifier has two benefits. First, yes it does ultimately translate into higher volume capabilities. Indirectly, it also means less distortion. As you run your amplifiers closer and closer to their peak levels, the more harmonic distortion they introduce in the output. So by having a more powerful amplifier, it allows you to run the amplifier farther below it's peak and still produce the same volume. This means less distortion. It also gives you headroom, which is the ability of the amplifier to respond to extraneous peaks (transients) in the signal without producing additional distortion or going into clipping (what happens when the signal exceeds what the amplifier can reproducel).
I hope that makes sense, it's a lot of information to try to explain in such a brief format, and it's late so I don't know how coherent it was.
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