Different amplifier class for different music genres?

Ralph (Atmosphere) is correct.  An amplifier is designed to amplify the input signal with expected 100% accuracy.  It is designed to operate with a flat frequency response over the stated frequency range into a designed for load.

There are other criteria, such as input sensitivity, gain, input/output impedance, etc.  But that is it.  

Some amps are designed for specific loads or specific speakers.  Lots of speakers have  some sort of wave shaping circuitry in their crossovers to  compensate for the peaks/valleys in the speaker's response.  This is why buying an after market electronic crossover that wasn't specifically designed for that speaker may not be a good idea.  Because the specific wave shaping circuitry isn't present.

An  amp designed specifically for a certain speaker, may have that circuity internal to the amp.  But, this is very rare.

So, basically, the amp shouldn't care one lick  what the signal is as long as it is within the frequency range for that amp.  The amp's output is suppose to be flat.  Basically, the input signal amplified.  That is it. Doesn't matter the genre of music.

Of course, "tuning" an amp to sound a particular way is another matter. The designer is actually adding circuitry into the amp to force the amp to reproduce the signal in a matter different that just amplifying the input signal.  Some add way too much lower end response (bass) or mid range or high end boost.  But if you graph the signal/frequency response of that type of amp, you will see over the frequency range that it is most definitely not flat.  Basically, they cheated.

An amp's output should be as flat as possible over the expected frequency range.

Again, it doesn't matter what  type of music is being played.

enjoy

The amps should indeed sound different anyway. Different design and circuitry.  However are we comparing apples to apples.

Are we swapping one amp for another in the exact same system (changing absolutely nothing else) and listening to the same music?  Also, did you match levels?  are the amps rated exactly the same?  etc.

The first error that I've encountered is that most don't treat this scientifically in experimenting. 

Listen to some music on the system.  Get a test cd/album.  play at exactly the same volume (in other words, don't change anything).  now get a DB level meter and measure the level.
now swap out the amp (or other equipment) (changing nothing else).  play the same test cd.  say 1 mHz signal or white noise.  measure the level.  now adjust the level so that it absolutely matches the level of the first test.

Now listen to the new piece.  People have a tendency to listen and interpret volume level differences as a good or bad thing when actually the levels weren't matched in the first place.  So the test is actually not equal.

Same is true for amplifier comparisons.  Are we comparing a 100 wpc amp with a 250 wpc amp?  if so, did you match levels first before the test?
Now compare the amps and listen carefully.  yes, different amps will sound differently in the same system (changing nothing else).  
I've noticed that people test on different day and swap not only the amp, but cables, etc. and even sources and then have the nerve to say that amp A is better than amp B.  

Also, I was referring to designers that place wave shaping circuitry into their designs to boost bass or other things.  You can tell easily enough by simply looking at the frequency response graph of the piece.  if it isn't flat, then yes, they cheated.

An amplifier is supposed to be absolutely flat in the frequency response.  It is only intended to amplify the input signal and produce and exact replica at the output without distortion, and it is suppose to be flat in the stated frequency range.  Say 20 hz to 20 kHz.  Should be flat.

Some are very bright.  Older Krells were bright to me.  They boosted the upper ranges too much.  Some amps had too much bass response.  People would listen initially and say wow!  that sounds great.  excellent bass.  But actually, it wasn't accurate at all.

But two 100 wpc amps of different designs will not sound the same even if played in the exact same system.  The circuit design will ensure they sound different.  Better?  depends on if they were level matched in the system first, nothing else was changed and then listen.

make the test fair.

enjoy.

Sorry, meant to write 1kHz signal, not 1mHz.

enjoy