I have a classic, had a 6l6 shiva but none of the rest. But here is my two cents if that helps.
The 6l6 shiva had an amazing woody tone, very natural sounding to the point that the gain sounded like it had a fuzz box running instead of pure amp gain. (kick myself in the ass for letting go even though I wanted more "high gain" tones)
The classic is more compressed than the shiva but its not overly compressed like my Diezel VH4S was. The diezel had so much compression that it took all the fuzz out of my fuzz pedals, they just sounded like mushy distortion. The classic is open enough to let a fuzz pedal sound like a fuzz, and delivers much higher gain than my shiva did. I wish the classic had dual excursion/presence controls and a boost for plexi mode like the 20th ann. but keeps all tone the sme as the classic (if that makes sense). I like the green and blue channel and the red channel (unboosted) on the classic with the excursion in loose mode but this makes the red channel (boosted) sound a little too boomy. If I roll off the bottom end to compensate, I lose too much chunk on the blue channel and red (unboosted). Based on how my classic sounds and the clips of the helios, I'd say the classic is more compressed than the helios but not by a whole bunch. The helios clips sound like they have a little more top end sizzle and saturation but a little less bass than the classic.
All that being said I have been thinking of finding a trade of my classic for a a 20th ann. X. I am scared to give up the clean channel of the classic though due to the difference in compression I had read about and heard between the two. So add that into the mix for this thread if you dont mind a little highjacking... Compare the Helios, 20th XTC and Classic!