Having played the GT games for over 10 years now, I am a big fan to GT Sport. IMO, GTS is the best all-around sim game on the market! It is the absolute complete package regarding content, experience, realism and authenticity. The driving dynamics are greatly improved in GTS from GT6.
I have recently starting playing Project Cars 2 (PC). I have to say it is a great game as well! The biggest differences I feel PC2 offers over GTS is the emphasis on the tire (temp, heat, wear etc.). This is a major element missing from GTS. In GTS you always have optimal grip. In PC2 the tires are cold at the beginning of the session, heat up as you drive, get hot and wear as you continue to drive/race.
In turn, I feel the AI drivers in PC2 are overly aggressive, cruel and is lacking. A couple major examples, if you are in a race and two cars in front of you bang into each other in a turn blocking the track, you will be penalized for going off track around them to avoid wrecking, etc. You will most likely be give 30 seconds to return the place X that you were in before passing them. That is BS! One of the first things you are taught in race school is to go off track to avoid a wreck or being wrecked. This is very poor on PC2s part. This also ties into how much of an absolute prick the AI Race Director can be. You will receive penalties for the smallest of mistakes, avoiding a wreck is one. He must be retired F1.
Both GTS and PC2 have different approaches, I feel. In GTS you smart of in regular cars that teach you and develop your driving skills as you go. PC2 I feel is better for people that already have a good understanding of track driving and racing to some extent. You also must have a bit of understanding of how to setup a car as well. The Loose setup IMO is certainly WAY to loose, and in combination with a bad steering wheel configuration you are in for a very challenging and miserable experience until you get things sorted. In GTS it is definably much easier all-around experience starting out. Just a few of my thoughts.
I have also tested the GT3 RS in GTS and PC2 on the Nurburgring GP track extensively and pretty much the exact same lap times - on street tires. The GT3 is more of a handful in PC2, the car does need to be driven slightly differently between the two games.
I know Forza is right there is GTS, I do not have any experience with it. Seems iRacing is the closest to a real "racing" experience, planning on trying it soon.