I have owned all three, but currently own the 20th Ann. EL34 version. Rockstarnick gave you a pretty good, concise rundown of all three, but I'll elaborate a bit more.
Starting with the EL34 Shiva, what comes to mind is a plentiful midrange, deep lows, and brilliant highs. I think of the midrange as "smoky," but like Rockstarnick and others have described before, you could say it's "hazy." To me it's kind of like a smooth grit in the sound. I have heard people describe the Shiva as fuzzy, but I wouldn't agree. Perhaps is the smokiness or haziness they're referring to. If Orange amps are considered "fuzzy" then the Shiva doesn't fit into that category. To my ears, it seems to have a great strength in the low mids which gives the Shiva a thick sound. It has a slightly more polite midrange growl than the typical British high gain amp like say a JCM800.
The 6L6 version is nearly as bassy as the KT88 version. If you compared the low end of the 6L6 and KT88 versions, perhaps it could be said that the 6L6 is kind of thumpy whereas the KT88 is kind of boomy. The cleans are slightly more brilliant with 6L6's. I wouldn't say the overdrive of the 6L6's lacks anything because it sounds quite good, but it has a different feel which is probably more comparable to the KT88 version which has been said to feel a bit "stiff." The breakup is not the same as EL34's so the 6L6 version naturally has an incredible sound from clean to light overdrive, but not as rich with more overdrive.
The 20th Anniversary KT88 version is immaculate. It's has a very deep, detailed, 3D sound. The low end isn't as tight as with EL34's, 6L6's are marginally tighter than KT88's. I wouldn't say KT88's are loose though, it's just a fuller low end with beautiful depth. I think the KT88 version is the most expressive sounding of all the Shiva models. It has an alive quality which makes it almost feel like less effort is required to make the notes come out. Sweeps and arpeggios roll off your fingers with almost an oily drip. It has kind of a squishy pick attack that feels a bit stiff because it doesn't have the chewy midrange of EL34's. The midrange is more balanced than EL34's and perhaps marginally less scooped than 6L6's.
The 20th Ann. EL34 version (which I have) is chewier, more vintage, and less wide than with KT88's. It has a spongy attack and retains most of the smokiness or haziness described of the EL34 Shiva, but also marginally more refined than the stock Shiva. The midrange is more aggressive than with KT88's. Also, the EL34's don't have the same wideness and separation that KT88's have. The cleans are pretty much the same as a stock Shiva, but you have the advantage of using the boost to get all kinds of clean breakup and classic rock sounds while still being able to use the tone controls (something the stock shiva can't do).
The 20th Ann. model with KT88's is a bit hi-fi sounding compared to the stock Shiva. With EL34's, it's more vintage sounding but still has a bit of the hi-fi quality. Modern mode, in my opinion is better than classic mode when the 20th Shiva is equipped with EL34's. However, the KT88 version sounds equally great in both modes. I can't describe exactly what it is, but there's something very subtle that's missing from classic mode with EL34's installed in the 20th Shiva.
When it comes to the clean channel, I would say KT88's are my favorite, followed by 6L6's, then EL34's. However, I wouldn't say any are better than the other. It's a matter of taste. I just think the KT88 version has more lushness and depth.
If there is any criticism to the KT88 model, it could be that it has an almost papery kind of overdrive in comparison. However, I have found that careful dialing of the excursion, mid and presence controls have a lot to do with that. The tone controls seem to be interactive. Turning up the mids seems to increase the presence, so an increase in mids requires a decrease in presence. I can't describe how the excursion control affects the tone controls, but it seems like if I just leave it off, it's hard to get rid of the paperyness at lower volumes.
I have also heard people say the KT88 version has more gain but I think it's a matter of attack. The KT88 version FEELS like it has more gain and more easily yields a liquid solo tone, but has no more gain than the 20th EL34. It has a stiffer breakup than EL34. The 20th Anniversary model (EL34 or KT88) has pretty much the same amount of gain available on a stock Shiva on the classic channel. It's the modern channel that has lots of gain.
It is said that the 20th Anniversary Shiva is designed around KT88's, but from some of the techy stuff I've read, the components used don't necessarily reflect that. I personally think it sounds awesome with EL34's. However, I have come full circle after all of this time and experimenting and decided that I will go back to KT88's or 6550's. Partly because I want to get back that aliveness that I perceive, and partly because my 101B gives me so many great EL34 tones that having two EL34 amps is overkill.
In any case, all versions of the Shiva are incredible. Summary:
The stock EL34 model is just an overall great, versatile, amp for clean and gain. It's the best with varieties of overdrive pedals for achieving different kinds of sounds.
The 6L6 model excels at clean, blues and classic rock. It has a great distortion sound, but doesn't have the midrange honk or high mids people like in a British voiced amp.
The 20th Anniversary with KT88's is a very different sounding amp that's alive and blooms under your fingers. It's wider from low to high, and more balanced in the midrange than EL34's (mid hump) and 6L6's (bit of a mid dip). It has a bit of a hi-fi quality, but still has a great sound for classic rock. It's very expressive so any kind of soloing or shredding really stands out.
The 20th Anniversary with EL34's is basically a 3 channel stock Shiva. It has a lot of gain in modern mode, tone controls that remain active when boost is engaged, and the Excursion control. It would be the choice for people who want a Shiva with more gain.
