If you used the same cartridge and phono amp, I am wondering how much of a difference would you notice between a mid level turntable and a higher end turntable. I would think part of the difference would be less vibrations? Hence the reason I purchased a Isoacoustic zaZen vibration reduction table for my turntable.
Given all else being equal - no difference....
But - differing materials, differing TT body structure, suspended vs unsuspended designs - these could all impact on the sound, and would be dependent on the room & building in which the TT was being used, in addition to the rack / isolation on which it was standing!
If the rack/room interaction was perfectly isolated, then the body structure and suspension would not be a differentiator (in other words these almost always make a difference.... whether for better or worse depends on the details of your setup!)
There there is the arm - if we assume both arms are from the same type... same length, and same effective mass, and neither arm has fluid damping (or electro-magnetic equivalents) - then no difference...
But if one of the arms was of a different effective mass to the other - then the interaction between arm and cartridge suspension, and the resulting resonant frequency would be changed.... resulting in changed sound... - whether better or worse, depends on which arm suits the cartridge better... if the cartridge were high compliance it would prefer the lower mass arm, if low compliance it would be in favor of the higher mass arm....
What about if one of the arms is a linear tracker !! - oooh - now whichever TT has the Linear tracker, will have reduced distortion at the geometric extremes - basically/typically with a standard tonearm there are 2 minima at which it is perfectly aligned and geometric distortion is minimised... the rest of the record surface has gradually increasing distortion as it gets more distant from the minimal distortion points...
A Linear tracker, will have the same distortion as the minimum points on a standard arm, right across the record...
Reality is, in most cases moving from an $800 to a $2000 turntable will merely be a change - unless you know precisely which weaknesses you are aiming to improve - the end result will be random - There are excellent $800 and $2000 turntables out there, and the synergy between cartridge and arm, as well as table and its mounting rack/floor/environment will typically have a far greater impact on the sound, than the difference between the turntables.... so if the move from the $800 to $2000 TT, moves you from one that does not synergise well with your setup and cartridge, to one that does... you will have a marked improvement.... and if it is the opposite, then your sound quality will equally degrade.
One of the joys and fascination of vinyl, for technically oriented gearhead geeks (like me), is the sheer number of variables involved in getting the best out of it - and much like hot rodding cars, the plebeian origins of the base chassis, can frequently be overcome to result in a high performance TT.... And vice versa, purchasing a ferrari, provides no guarantee of outperforming a properly fettled basic mass market sedan. But it does give you a head start, in that sometimes the engineering is superior in the more expensive TT.... however even that is not guaranteed - there are plenty of boutique manufacturers who charge vastly more, for something which in fact is no better.... and there are many Caveat Emptoriums out there selling these.