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

Matching and preference will play a role which one you like.

mulveling, "ain't cheap" is an understatement, VAC's top and near top of the line separates are extremely expensive, but you say they are worth it.

I have no complaints regarding the dynamics and bass of the VAC Avatar SE EL34 based integrated. I suppose, it also depends a lot on particular signal tubes that you use. These 60 watt/ch in ultralinear mode sound quite powerful.

So, there is something inherently very musical in EL34/EL84/6L6 tubes.

I love the sound of EL 34 tubes, reminds me most of tube amps from the past.  A ripe romantic type sound but without any bass slam. 

@yogiboy 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!

+1 yogiboy. 100%, so true. Was just sharing this on another thread about this, its a fact. Matching to your preferred sound is key, all speaker dependent for sure.  

Agree with most posters here, EL34 easily my favorite push pull amp tube. Sweet, natural mids, highs may or may not be rolled, depends on amp, bass is biggest issue. Bass issue is lack of slam, can be too resonant in some situations. Power supply in amp/speaker choice key here, get this combo right and bass can be ok. Still any KT will beat it on slam, extension, problem with KT is never get that same sweetness, natural mids, highs can be pretty nice, mids are the issue for me with KT.  I also generally agree the lower power KT sweeter than higher power.

In the end, the EL34 and push pull didn't do it for me, transitioned to 845SET than 300B SET. 300B is a magical tube with the right speakers and properly engineered power supply in amp, with this no roll off in highs, no soft, overly resonant bass, some totally misguided on stereotyping 300B sound. The boutique 300B tubes absolutely necessary. Running 300B in parallel can be replacement for those running EL34 with speakers SET can't handle, some very nice amps in this category out there.