First thing I'll say is that the game is FUN. Maybe it's just the new game feeling or the anticipation - but whatever the reason - the game is FUN. My BIG 3 categories for the game are Physics, AI and Graphics.
I received 3 cars - Mitsubishi Lancer, Hyundai Genesis Gen. 3 and Hyundai Genesis Gen. 4. Physics are the most improved aspect of the game over GT6: Handling is sublime, you can really feel the weight difference between classed, the weight of the car in turns, the sense of speed, acceleration and braking. I love flying full speed into a corner (against better judgement), slamming on the brakes at the last second, hearing and feeling the car backfire, and accelerating out of the corner just in time to miss the grass or bumper.
I have never been a huge Tuner, so I did not attempt to tune any of the cars. In addition, I played with no braking or steering assist.
The AI: I played 5 or 6 races on Intermediate in Arcade mode against the AI. In intermediate mode the Grid position I started in was 12th every time. I feel like the AI is slightly improved over GT6. The "rabbit" leading the pack was not always present, as 4-5 cars jockeyed for 1st place in a few of the races. And in viewing the replays, I did see cars behind me did in fact spin out on occasion. But Grid racing is sooooo much better than Rolling Starts. I hope PD keeps Grid racing as the default or at least an option.
The graphics are the least impressive aspect of my BIG 3. They are improved over GT6, but only slightly IMO. Still, the graphics are good, just not GREAT. Mind you, I am playing on a 50" 1080p 240Hz tv, no HDR and no PS4 pro. I am curious as to what the game would look like in 4k with a PS4 pro. I felt like I noticed jaggies along the roofline of the car, but at the same time there were little touches (lighting, air balloons, slightly improved crowds) that brought life to the graphics that have not previously existed. Also, when I spun out out on the dirt I noticed (in the replay) a guy on the sidelines waving a yellow flag. Nice.
Online is something I care about least of all, but I did get one game in on Sport Mode, and again I do not have PS Plus. I was disappointed that I did not receive a "sportsman grade" or something like that to assess my driving style, but other than that, online was fun. Hopefully PD assigns rewards or incentives to clean racers.