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

in my experience:

in General, Absolutely.

The VAC 80/80 was KT88s, good sounding $2,500 amp but it chewed up KT88s, and it bias drifted. I had an MV52, that was sweet, perhaps beige like the front panel, but lacked any real punch.

I also used a VAC Ren 30/30, gorgeous but it chewed up 300Bs and a Ren 70/70 - outstanding in every way but broke the bank chewing up 300Bs - 8 at a time!

I still have the 30/30 (no tubes), it has something awry as it makes very unpleasant noises, probably a cap is blown!  I met Kevin Hayes at Sound by Singer (early 2000s), he opined that the 30/30 might have been the best sounding amp he had ever designed, but it was not a commercial success, he could not sell it for a price that was profitable.

Some people will just listen to 300B based amps and nothing else, I heard.  They consider 300B to provide the purest midrange of them all.

RM-9 wrings quite a bit out of EL-34 but Roger was a genius… Like Gordon Gow and the 6L6 MC240… but really no meaningful conversation is possible without also considering the massively important imo ….output transformers…. 

IF a VPI magic brick on the output xformer significantly alters the sound for the better, you know they skimped…..