high voltage does makes a difference in tube based pedals.
Some pseudo tube pedals with yellow LED light show that runs on 9VDC are running on starved voltage. Its still distortion but hey hey... if you like that sound, no one can fault you. Us snobbish techies will keep saying otherwise... cos we're uptight and snobbish like that.
However there are preamp tube based pedals that actually runs on high voltage. These variants can be simply looked at as taking the preamp section of a REAL tube amp and stuff it into a box. Take out the output power tubes, big ass Output transformer and big wooden cabinet.
Take for example the EH English Muffin. Its being fed with a 12VAC power supply into a small transformer in the PCB to scale it up to 300VAC. YUM YUM. Does this preamp sounds like a vintage Marshall amp? I don't really think it does but then do I have the rest of the complementing ingredients like a tube power amp into a nice cab? NO. So who am I to say this or that?
It could be an EXACT copy of a Marshall preamp and I believe it is.
You can mess around with the preamp tubes. There are loads of them out there. 12AX7 AFAIK have the highest gain. There are 12AT7, 12AY7, 12AU7 that goes even lower in gain. I've played around these tubes with the EH English Muffin and had a lot of fun hearing how these tubes interact with each other. In the end, I prefered the sound of the low gain preamp tubes in the English Muffin.
There's no right or wrong in sound. Its whether you like the sound or not.