Different amplifier class for different music genres?

IMHO: At a price point, maybe. If you need a lot of power at a good price, Class D does that. Class A does not. I think matching the amp to the speakers matters more than what you listen to. I had a Class A ARC Classic 60 that was glorious but I missed the oomph of my Moscode 600 Maxi, and I've finally decided (after 50+ years of this hobby) that having enough power matters a whole lot. (At the moment, I have an ARC VT100 driving Vandersteen 5s, but they have built-in powered subwoofers.)
And I think all amplifiers sound the same... until you connect them to speakers.
Good luck, and have fun!

@atmasphere, the most common myth? That might be a tiny stretch. Lets just say one of many:-) 

There is no difference in the power needed to reproduce an orchestral crescendo as there is needed to reproduce Slipknot. A good amplifier speaker match will play anything. You can not talk about the amplifier without talking about the speaker. The two must match. There are amps that will drive anything. They tend to be big expensive bruits. While a SET amp may sound OK on certain very efficient loudspeakers it will die trying to drive Wilsons. An amp is going to sound different depending on the speaker it is driving and a speaker is going to sound different depending on which amp is driving it although there will be some basic characteristics that won't change such as dispersion and imaging. 

The most common myth? That might be a tiny stretch. Lets just say one of many:-)

The reason I say that is because of how many times I've heard that JBL L-100s are one of the best rock speakers out there. This where there really isn't anything a speaker manufacturer can do to make the speaker favor a certain genre.

Greg_f, I am a class A fan. I also like big powerful amps. However, class A/B has come a long way. I have not yet heard a class D amp that thrills me but there are many available I have not heard and from a technical standpoint I see no reason why they should not be capable of first class sound. I have not used a Jeff Rowland amp and he has many fans. 
Your Mahlers are very intelligently designed speakers. Suspending the tweeter is a novel thing to do. They are 6 ohm, 90 dB/watt/meter speakers. A Pass XA160.8 would be wonderful as would Parasound JC 1+s or Atma-Sphere MA1's. At the less expensive end are the Parasound A21+, a killer amp for the money. The Anthem STR is another relatively  inexpensive powerhouse. It is always better to overpower a speaker than underpower one.
 

Thank you all. You learn every day. It has been a long time I was wondering if my amps have synergy with my speakers. I am not prepared to change my speakers at this point so I would like to try different amps.

@mijostyn. Thanks! It sounds like you know my speakers. Yes, they are well designed but could be difficult to drive, they are nominally 6 Ohm load but they do drop below 4 Ohms at some low frequencies. 
Now I need to decide if I want to 'just' change the power amps or go the integrated route.