No there isn't really. People speak of knowing what an 'LP12' sounds like but it needs to be more specific because if you compare an early one to a recent one you'll find they sound markedly different. The LP12 has been in constant development for almost 50 years now and the sound has changed significantly in that time. So be careful whose opinions you read on the LP12 as you really need a frame of reference on what kind of LP12 they have experienced. Even then, their ears, not yours.
I'll try to answer your question though, because I've had Rega's (P2, P3), many LP12's (almost 20 of them over the years from 1974 spec to 2021 spec and most varieties in between) and lots of other TT's from the likes of Technics (SL1000/SP10), Thorens (many TD150, 160 and 320), Pink Triangles (all versions including the Anniversary), the Voyd, Gyrodeck, Revox, Lenco's and latterly a monster TW Acustic.
Firstly any LP12, (if in good fettle) will be significantly better than a Rega P3, even an early red button 70's spec Linn. The Linn has a better bearing and superior isolation. It's always been an upgrade over the Rega deck. The Thorens TD150 and 160 are nice decks and similar to the Linn but again the Linn betters them primarily because of a better bearing assembly. It's as simple as that.
Early LP12's of the 70's and 80's have a warmish tone, yes its rose tinted and coloured with a big, bold full range sound that's most beguiling. A lot of people really like it. Downsides? The stereo image is a bit diffuse in modern terms and they are not terribly detailed. They are great fun to listen too though. I preferred the leaner more detailed sound of the Pink Triangle tables in the late 80's though I have to admit. Linn invented the 'tune-dem' so try to keep customers off the detailed and accurate scent and focus on the mid-range hump instead because it brings a false sense of timing, you focus on the beat. It makes your foot tap. The tune-dem is absolute non-sense of course but hoards of acolytes still believe in it. Its a cult and it does not help matters at all when trying to understand the LP12.
The mid 90's saw the LP12 sound take a change of direction. There had been steady improvements in most of the major components upto that point but the Cirkus bearing and Lingo power supply moved the game on for Linn and modernised the sound. The bearing brought a much tighter bottom end because the mid-bass bloom had all but gone with much improved speed stability from the Lingo. A lot of people disliked this new direction because it sounded more like CD of the era but the truth is the Linn was just digging more information from the groove. Everything was better, particularly with the Ittok or Ekos tonearms and a Troika cartridge. In fact a mid-90's LP12 started to sound much more like a Pink Triangle Anniversary, or a Voyd than Linn would have anyone believe
I'd still give the nod to the Anni or Voyd on SQ alone of this era though ;-)
Since then Linn have continued to steadily improve the components and developed a three tier range. The bearing was recently improved again with Karousel which is more detailed than the Cirkus but still has the 'swing' of the pre-cirkus bearings. Its a fundamental improvement for any LP12. The sub-chassis have improved significantly too and none of the LP12 versions use a variant of the old pressed steel subchassis anymore. The Majik sub is a folded aluminium, very solid and nicely made mated to a traditional laminated armboard, the Kore take this a step further by integrating a machined aluminium armboard and finally, the one-piece CNC machined from billet Keel sub is a world away from the pressed steel sub of yore. This is where the LP12 has changed significantly and why the sound has changed so much. They are good, better, best but all of them bring a much more modern sounding LP12. Much more detailed, much better soundstage, better decay on notes, better and more textured bass etc etc etc.
Finally the power supply and motors have changed a lot over the years too. The first LP12's were powered from the mains with nothing more than a resistor to drop the voltage for the motor and a phasing capacitor to alternate the supply to alternate phases of the motor. Same as a Rega. Same as a Thorens. The Valhalla of the late 70's to the early 90's is far superior and regenerates the AC reference to its own 50Hz oscillator. The Lingo that came in the 90's (and the Lingo 2 and Lingo 3 - all basically the same) are external and more complex supplies with more mains filtering and torque management of the motor for lower motor vibration. The modern decks again have a good, better, best tiering on the PSU's. The 'Majik' supply is quite basic and similar in concept to the original red button supply, but built to modern safety standards! Still using a modern version of the classic 'Airpax' 110V 24-pole AC motor though. In the Accurate spec the recent Lingo 4 brought an entirely new AC motor and a feedback control for motor stability, quite an advanced supply. The 'Klimax' spec decks have a Radikal power supply which is a DC motor, again with a feedback back loop off the latter - it can also power an internal phono stage called the Urika
I won't go into the arms and cartridges but its a similar story of development and culminating in a good, better, best tiering. Its worth mentioning that modern LP12's set up much more easily than older ones, primarily because the components are better machined and more consistent. Its so much easier to get the pistonic bounce on the suspension and it stays where it is over time too - older ones used to easily 'go-off' if moved or with time requiring periodic visits to the dealer for service. You'll always need to periodically change the belt and oil and a tweak off the suspension on any suspended deck is a good idea but a modern one will go longer between services than they used too.
I can tell you that at each of their price points, the latest LP12's are absolutely competitive. It's true they are all expensive but then good Hifi is these days. The £3.5K latest Majik spec deck does not sound the same as an 80's LP12. It really really doesn't! It sounds like a modern £3.5K turntable should. It's excellent.
The £7K Accurate spec deck is really expensive but again its competitive with other brand new record players at that price point. It is significantly different from an 80's LP12 - a whole world away. As far apart as a 1985 Porsche 911 is from a 2021 911! Compare the bearing, sub-chassis and power supply to its 80's equivalent and of course its better. Shit loads better.
The £15K 'Klimax' LP12 is a pure 'Veblen goods'. Luxury priced for the well heeled. It's better than an Accurate for sure and is genuinely a high end record player now but you know the law of diminishing returns kicked in long ago. It is properly high end level.
The aftermarket complicates things a lot and I've heard and tried some real shit and some real good components. Its a crap shoot though and is no different to hot-rodding your car - basically you are on your own and your particular blend of components may or may not work the way you want. I once built an LP12 with all of the forum shilled favourite aftermarket upgrades of the day and it was awful - absolutely terrible. Stick to the Linn recipe, or something close and you won't go far wrong in my experience. There are some great aftermarket upgrades, and I do use a few myself but be very selective. Basically, if Peter Swain (Cymbiosis) stocks it, then it will be good.
Many years ago I got sick of the forum know-alls and decided to hear these things for myself and I've made it my hobby to enjoy as many turntables, arms and cartridges as I can but somehow got obsessed with the LP12 along the way. In that time I've compared LP12's of all levels against their contemporaries and have always thought the LP12 has been a competitive turntable through the decades. The LP12 has never ever been the best turntable in the world though. Is there such a thing? There has always been higher performing decks, then and now but its a great deck with brilliant support and with a healthy choice at all price levels. There is an LP12 that will satisfy most people. It's a truly great product and is an icon for good reason.
The last few years in particular I've built and owned a lot of LP12's for my own amusement and have tried to collect the classic variants. Some have come and gone, normally because I end up with too many on the go, but they are all very good record players in their own way. At any one time I've usually got 5 LP12's on the go and its all just to satisfy my curiosity. Consequently I've become a dab hand at servicing and restoring them, its become a hobby within a hobby. I am a disciple of Peter Swains set-up guides and follow his builds across the forums for tips and he's been enormously helpful to me. By much practice and following Peter's method to the letter I've got constantly good results now. I've had a few basic LP12's from early red button 70's examples with Grace or Basik tonearms, mid-range 80's and 90's decks with a variety of tonearms (including Rega's), the modern Majik and Accurate level decks and latterly one thats near Klimax level. I've also got the classic 'Naim' LP12 too with the wonderful combination of Armageddon/Aro/Troika.
For anybody interested in the LP12, owner or would-be owner, I would highly recommend the Linn Sondek LP12 facebook group. Its a really good bunch of folks, tolerant of the Linn way or the aftermarket way, fiercely knowledgable, incredibly helpful and musically inspiring all day every day. It's not remotely like the old cult-ish Linn forum. Thats my take on the venerable Linn anyway.