3. It is very important to understand the condition of vintage TTs
4. Listen, listen, listen to both new and vintage TTs before forming an opinion
At this point I don't see a general consensus due to the limited number of folks who've done the direct comparison but I hope others will chime in. Thanks!
I once worked in audio sales where I had a chance to compare turntables customers already owned with new models they were curious about, but this was about 20 years ago, and our entry-level 'tables were models like the Linn Basik and Revolver (no one liked their old turntable better). More recently, I've been able to demonstrate the superiority of entry-level Music Hall and Rega turntables to friends who were skeptical that it could make a difference.
Part of the problem on getting a consensus on any given piece of vintage equipment is variability of condition. Maybe a 30 or 40 year old turntable, when new, would have outperformed a new, entry-level deck, but the things that make a sonic difference in turntables are all subject to wear: platter bearings, arm bearings, drive system, suspension parts, and even the body that holds it all together could be compromised by glued joints beginning to dry and separate. One sample may sound great if it has relatively low hours of use and was correctly maintained; another identical model may sound bad if it was abused or is simply worn out.
With vintage there's no way to know that your turntable is performing as new, but if you do a comparative audition, you can at least tell whether it's current performance standard is one you're happy with. But even then, how much longer will it keep that performance level? With a new turntable, you can expect that it will perform to factory-expectations, and it will likely maintain that performance for 15 to 20 years. If you start with something already decades old, how much more service will it give you? If you're looking for a turntable to make you happy for the long-term, I'd buy new; if you're looking for something to get by with for a while, then a vintage model could be a good solution, provided you have a chance to audition it first.
edit: there are older turntables for which new parts are available, so if anything is wrong or becomes a problem, it can be fixed. One example is the Linn LP12. Any of its parts can be replaced and the deck brought back to like-new condition. That may also be possible for other brands, like Sota, VPI, Rega, etc.