There are a lot of variables at play but overall, yes, the genre can make a big difference. Some systems just do better on certain styles of music.
A friend has a big, expensive system that I'd describe as dry sounding. For whatever reasons it sounds pretty nice with classical music and that's his preference. It's boring as all get out on jazz and it absolutely can't do justice to rock. He put on Pink Floyd The Wall a while back and it amazed me how removed I felt from the music. It was loud and it did a bunch of audiophile things pretty well but it was just impossible to connect with the music. Can't say I've ever been bored while listening to that album before.
I remember listening to that album on an old set of JBL's about 40 years ago. Those speakers were anything but flat, and a recording of a female singer would have you running from the room screaming. But those speakers played The Wall as if they had no other mission in life. Astounding.
Another friend claims that if the recording was made in the tube era it should be played back on tubes. 50's and 60's jazz comes to mind.
One of my old systems was amazing on jazz but didn't have the power and drive to do justice to rock. But you'd melt listening to it play jazz.
If my taste in music was mostly rock, edm, or other styles that tend to get played pretty loud it'd be likely the system would be different. The speakers would likely remain but the amp would likely be far more powerful simply to match the needs of the genre.