Interestingly there is a local shop where I live in Nottingham UK with a GT trio that's gathering dust. I might make an offer spare cash permitting, I think they have matching GT power amp too.
A solid state power amp will amplify your preamplifier's distortion tones. A tube power amp will give you the possibility of running your preamp clean and your power amp in overdriven mode - if you do this you'll get a sound that no preamp distortion can give you. The sound is spongier and has more 'give'. I used to run a 12U rack for guitar alone, which had a Triaxis and a JMP1 and a third preamp I made myself that only did one distortion tone. This was my setup in my commercial recording studio. I ran all three via MIDI switching (via a ground control) to a Marshall EL34 50/50. My recording studio was a soundproof concrete structure, so I could run the Marshall amp on full and the Triaxis on clean at 3 am in the mornng.
It was my favourite recording tone. It won't give you Satriani, but it will do a Santana type tone and it will do a Stonsey tone or a Vox type tone no problem.
I sold all of that 12U rack stuff as I do not need that much distortion in my life (!) and now use a F-1X for guitar (also use one for bass), which I run clean and run a tube power amp on full. The F-1X has a much lower noise floor than the Triaxis, and you'd get a nice power amp distortion if you feed a nice power amp.
I think actually a lot of the classic guitar combos in the 50's 60s did not have complex preamp cascading gain stages and the distortion was really an overdriven power amp stage.
Having said all that, I gig on guitar with a couple of cascaded TS 808s , a F-1X and solid state Carver power amp, and sometimes a Stewart power amp. the EL34 50/50 is a bitch to carry and my left toe can testify to its weight. The 20/20 version has a reputation for overheating, though I think they fixed that now. I did a series of gigs on bass with a guitarist who used one of those and I'd say that's all you need on stage for most bands.
It has less sonic bottom than the 50/50 though.
Mesa Engrg also have a slew of power amps, and I am looking to get either the marshall 20/20 or the equivalent Mesa 1U unit. You'd have better luck with Mesa in the US, they are terribly overpriced (even at used prices) in the UK.