Are EL34 based amps more musical than KT series based ? Or it's purely a matter of design?

I think that it might be a matter of taste. 

On my Quicksilver amps I can use both types. I prefer the sound of the KT88 compared to the EL34. It all depends on the speaker that you are using. I find that the KT88 sounds bigger and brighter than the EL34!

https://upgradehomedevices.com/kt88-vs-el34/#:~:text=Bass%20of%20KT88%20and%20EL34

IMO purely a matter of preference. I have sets of both, but generally lean towards the EL34 sound… finesse over power 😉…

There's a bunch of variables involved.  It's a matter of preference, the brand and age of the tubes, the unique circuit it's playing in, synergy with the system, and a whole bunch of other stuff.....definitely not an absolute.  It's also one of things i love about using tubes....try a new tube, and discover a bunch of new subtle tonal characteristics.