Which models? Those without speed control used a machined pully keyed to the mains line frequency that the synchronous motor 'locked' to. There should be no big variation among those models, as long as the mains is stable and as long as the pully/idler mechanism remains intact. A large stack of records on the platter could add an additional load to the drive system.
Variable speed models (Z-100) used a tapered pulley allowing the idler reduction disc to move up and down the shaft (for adjusting speed). Since this entailed a spring loaded mechanical connection, speed drift was not uncommon as the idler could move up and down on the pulley, over time (although it was usually gradual and not very noticeable, if at all). Someone with perfect pitch might recognize the variation on certain music, I'm sure. Wow and flutter was generally below most folk's perception threshold; rumble from the idler drive tended to breakthrough at times. At least that is my experience.
In order to accommodate the smallish motor (and come in at a price point) the SL series used lightweight platters. So you didn't get a larger mass flywheel effect.
By the early '70s, with the introduction and popularization of electronic servo circuitry, all the mechanical stuff became obsolete. Additionally, changers were no longer in fashion (however I believe the Garrard GT-55 changer used an electronic servo, and the BIC 980 had that, along with belt drive). Now, 50 years on, the strictly mechanical Garrards (and many of the others) are likely still working, whereas electronic servos from the era probably require servicing and/or electrical parts replacement.
One of the bugaboos of Garrards (and their like) is the grease used for the mechanical Rube Goldbergish gears and levers. It hardens, and that needs to be cleaned up--a labor intensive task. Also, with the exception of the Z-100, there is no way to adjust anything like overhang or offset-- that was fixed. Arm height adjustment was out of the question, although some of the later Duals provided arm height.
I would think that one of the moderately priced record players sold today would be at least as good if not better than any of the old changers. What you won't get (usually) is 78 rpm and the ability to stack records. Those are probably not important to anyone today. It would surprise me, however, if the cheaper belt drive record players have speed consistency that is appreciably better than the old machines. Once you get to quartz PLL it's goodbye Charlie.