No one can tell you the exact differences; too much time has passed since the PP's heyday in the late '80s. I once worked for a fellow who went on to run in the recent past Head's US sales/marketing division, and he didn't know. His short answer would have been that they were the same, since the Classic gets its classic moniker based on its being a copy of the Pro. I think your looking for more of a detailed answer, though.
Having used both, I think the Pro's feel was a bit more flexible in the shaft than the Classic, with a livelier stringbed and ballfeel as a result. The original Pro has alot of spring for a 90 with a tight string pattern. The Classic 600s that I've owned/tried over the years have had a bulkier, stiffer overall feel than the Pro, with a deader ballfeel. Could be in my mind, but that's how it felt.
There's probably something to the theory that Head abandoned the use of Twaron with or even before the Classic's intro, and simply tried to repeat the Pro's feel with a simple graphite/glas cocktail instead. Head no longer bragged about its use of Twaron as an ingredient, and that tells me something about whether or not it was used. That said, the Prestige 600 (1992) didn't mention Twaron on the frame, but industry reviews of that frame published that year all stated that the 600 did have Twaron in it, so who knows. Twaron's inclusion is relevant because it's a 'feel'/damping fiber, which could have largely accounted for the great feel of the original Pro.