When the "Classic" first came out I had one to review and keep for about 6 months before sending it to a friend in Germany, overall it best equates to a post '2000 Gibson except for the neck profile, which is slightly flatter and reminds me a bit of a '76. The body is modified with a greater lower 'bout cut and is thin like a Gibson, the headstock is small as are the tuners - These are really nice, they play well, have a more contemporary tone and are a very solid value.
I have a new Vintage Pro, first, it shares nothing with the Classic other than looking like a Thunderbird, the body is thicker, and shaped slightly different, headstock is larger of course, for me the neck is noticeably different, much thicker front to back. The pickups and hardware are of course meant to be like an early '60s issue Bird, tonally it's close to a couple of 'Bird that I have with Mike Lull '63 Spec pickups. Again, a very nice bass, quite different from the Classic.