Just picked up the game today, and here's my short thoughts. I liked the intro to the game, very nice, albeit a bit long. The menus seem much sleeker over GT3, and everything is laid out very nice. I don't care much for the running starts, which so far seem to be in 95% of the races. They are too long, and I found myself telling the game to come on while waiting for it to give me control. I don't care much for the blur effect when you hit a wall hard or another car hard, it takes me out of the game for a split second. Not quite sure what to say on the "improved" physics, only that I'm not qualified to say if they are better or not. It controls just as good as GT3, which is a good thing. I like the new tracks that I've seen so far, and I'm glad to see some old ones untouched. Your home has been overhauled in GT mode, as you can now actually see you car sitting in a garage (which is a nice touch).
Lots more to say, I just don't feel like typing. For those sitting on the fence on buying this game, I can say it's basically a suped up version of GT3 and nothing more. Photo mode is outstanding, haven't tried B-spec mode yet (although I don't see the appeal), and the GT mode feels identical to GT3. You can't go wrong with GT4, but casual GT3 fans may be turned off at the similarities between the two.