You also are a tonelab player, right?
So here's my very blasphemic question: how would you compare the modeller to the Shiva? (I know they are two totaly different things, but anyway...)
There are no stupid questions, only stupid answers:)
So comparing the TLab to an amp, is actually not so easy. I would say at VERY low volume, the modeller (and especially the TLab) will be more convincing. So for these moments before sunrise if the kids are asleep, there's no real use in firing up a 100W full tube stack to play on 0.001 level.
The big difference comes with a band situation and/or proper volume, where the full tube amp (and especially a top of the line one like the Shiva) will respond so dynamically to your playing, like the modeller never would. The tube amp is just so much more touch sensitive, organic, alive. It sings with so many different voices.
On the modeller you can find a sound that sounds great no matter how you play, with a cranked tube amp this is becoming much more difficult - but also the payback is much higher, you get such versatile, dynamic and punchy tones - from a modeler i haven't heard anything yet that comes even close.
However, if you mic a tube amp and record its signal and put it in the context of a song, where tracks will be compressed and EQed and effects added, the remaining difference will be very small.