Very interesting question - I can only speak from limited experience, and from what my ears told me.
I went from an LP12 to a Gyro to a NAS Spacedeck, each time the sound of the system changed fairly radically.
The LP12 was a pre-Cirkus (this was back in 1991 after all) one; moving to the Gyro the sound lost a fair amount of heft but gained in detail and spaciousness. I preferred the Gyro - at a push - but it was quite close. The much bigger change came with the Spacedeck. This had a very relaxed presentation, but was quite uncanny in that there was no loss of momentum, musically. That's to say, the vehicle was always making progress, moving forward compared to the more 'let's pull over and stop...take a look at the pretty scenery' presentation of the Gyro.
The Spacedeck seemed to take a lot of what the Michell brought to the party - a big, expansive sound - but (apologies for the dreadful cliche) it really was the iron fist in velvet glove. Probably the first turntable I've owned in 30 years where I
truly forgot about the hardware and got really immersed into the music.
Out of the 3 turntables, if you were to ask me which one I'd like to have back, I'd take the NAS followed by the LP12.
As to their house sound?
LP12 - forward, ballsy, plenty of drive, coloured.
Gyro - spacious, fleet-of-foot, detailed, slightly mechanical.
NAS - spacious, big, fast bass, creamy*, relaxed but dynamic, slightly dark.
Sorry I've not really given a particularly good answer to the original question but these are the 3 turntables I had to go on.
*The NAS is a really 'full fat' sounding turntable. Lots of (good) colour. I loved it, and would have another one if I could afford it.