I agree, HP2 had many redeeming qualities but also showed signs that some production values were lost.
(Drifting off into anal retentive mode here. Sorry.)
One thing I disliked was the spoiler not popping up on the 996 Turbo, or on any other cars for that matter. Both NFS II and Porsche Unleashed blew my mind by having the appropriate animations for such aero features. The steering wheel didn't turn with the driver's hands on the PS2 version too.
Another thing I disliked was the cheapish feeling menus and the selection sound effects, whether the PC or PS2 versions.
And the detailed car showcases were scrapped too, though there was a commentary at least.
On the rest:
TNFS) The original was amazing. I felt there was the greatest 'connection' to the real cars thanks to the brilliant specifications and commentaries by R&T compared with the Test Drives of that time.
From today's perspective, I feel that the car list also showed the respect the US magazines had for high performance Japanese sports cars contrary to what some may feel today about such vehicles. (Reading up on review archives of the other major magazines regarding such cars backs this up too.)
The usage of photo based textures also made the cars and environments feel more 'real' to me. (A literal example of photo realistic graphics perhaps.) The physics feel 'right', if not totally realistic, even by today's standards.
II) Personally felt the problems with this one was that it felt a bit arcade-ish and the showcases weren't as detailed. Still, it had nice graphic effects with Glide, fun choice of exotic cars and locations and of course, active aero.
HP) Bringing back cops made this one more fun. Physics were a mixed bag as it felt more grounded in reality but also annoyingly floaty. I would describe the car list as 'expensive' versus II's 'exotic to the point of non-production'. Graphics were very good and the location design and commentaries were excellent as usual.
HS) I liked the career mode. It was one of the few times where there were added financial penalties for crashing. There were performance modifications that affected appearance too. The car list excluded concepts but had goodies such as the E39 M5 and the 993 Turbo.
Having found a Win 7/modern GPU patch, another thing I discovered was the official EA produced HSV, XR8 and R34 GT-R featuring in versions sold in the origin countries of the respective cars. There was also official DLC including the 360 Modena, Z3M Roadster and Coupe, Lister Storm and updated versions of the DB7 and XJR-15 from HP.
One of the few things I disliked was that there was slightly too big a gap in performance between the Z3/SLK and the next tier with the Camaro/Firebird and the rest. Physics were carryover as well while the PSX version had the much more advanced PU physics engine.
Another issue was a lack in locations to the point where the HP ones were included as a bonus. None of the new locations really had the uniqueness of some of the HP tracks either.
Still, I loved the menu design and soundtrack. It just felt, well, cool.
PU) To be honest, even this game has some bugs. However, apart from a few relatively minor niggles, this game feels extremely, stupendously well put together. This probably ties with the first for my favourite of the classic titles.
It just felt quality, with well designed menus, features like the history wall and the videos and the then high detail car models inside and out. (2001's GT3 on the PS2 would be a leap in car exterior quality.)
The best part was the 2 types of career. The 'money' route was a lovely trip through the years while the factory driver mode previewed many of the lovely high performance Porsches and the brilliant driving physics of each car.
It's really only by today's standards that I can poke really picky holes in the game. For example, the 996 models having the 986 Boxster S 5-spokes instead of the correct design that resembles the design introduced with the 993 Turbo. The 993 models had poorly aligning dash boards too. (The speedometer should be dead center relative to the steering wheel.)
Also, some significant cars were conspicuously missing. The 356 No 1, non turbo G-models, 924s, most 928s and 968s for example.
But still, not a single driving/racing game gets every detail perfect, even today. PU and the original just felt light years ahead of the alternatives.