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

If midrange is not right, the rest doesn't matter.

Power cord can make quite a difference for dynamics and bass, by the way. I use older Purist Audio Dominus Ferox, appears to be a perfect match.

Absolutely correct about 300B amps. So much is the power supply. In fact, it took an expensive, properly engineered 300B amp to open my ears to this tube as viable. Have never heard a good 300B amp for less than 15K. 

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.