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 😉…