You ask an interesting question. I have heard both tables, not in my system though. The Linn is the table that I own, if that tells you something..
The VPI Classic is a nice sounding table with some decent attributes...the basic model was priced at a point that I thought it could compete well with its competitors. The more expensive models..not so much. The Prime and Signature, to my ears were not as ‘expressive’ as the Classic models.
The LP12, and this is highly dependent on the version, are, again to my ears, more accurate and consistent to the sound of what I hear in a “live” setting vs. the VPI’s...and seem to have better ability to get closer to what I consider is the ultimate in home playback...master tape.
You will get many opinions on the difference between the tables you inquire about, only you can decide for yourself which one you prefer...and remember, the tables vary greatly by what consists of the particular model, age, set up and numerous other variables.IMO.