One thing to remember is to pretty much never talk about your real on the road experience when comparing it to the game. Unless you are a seasoned race driver your real world driving isn't going prove anything over the game simply because in real life you drive with apprehension. You do not drive you do in the game, no one hammers the throttle coming out of corners or brakes late and deep into a turn...how would your everyday driving compare to anything you do in the game?
The game is attempting to simulate complex behaviors in vehicles, there are some issues with some cars that relates to their steering rack and not the actual game physics Audi R8 LMS Ultra springs to mind. For the majority of cars' I've driven they handle relatively ok and ask for your attention. While I have never driven those cars in real life, it's assured that someone who had a hand in creating the game did. The physics of the game is global so it's just plug in values and the calculations take car of the rest, so if the physics were broken then every MR would reflect that...but they all have varying degrees of difficulty. That breaks the idea of physics and it coming down to something more specific with each vehicle I'm not saying the cars are perfect nor are they broken but anything is possible.
What I say is to learn to drive each drivetrain type, but do not assume because you drove it before means you can handle any drive type with ease. This is possibly the thinking leading many drivers issues with cars in the game, all cars are not equal nor do they all handle exactly alike. MR and RR cars tend to be the most difficult to drive fast because they require utmost attention, they do not behave like FR cars so you cannot drive them the same. The majority of their weight is behind the driver which is a boon because it allows the car to turn very quickly also it will cause loss of control because the car is very easy to turn. Doubled Edged blade is what MR cars and RR are because their nimble handling requires greater attention the harder you push the car. You have to manage tire load and weight shift, steering angle, brake and throttle inputs. Going in a straight line is the easy part, managing the balance of the car through a corner isn't as easy though. It takes some learning to deal with it, but it can be done.
Now we can draw PD's attention to some cars with odd steering issues LMS Ultra '12 turn excessively to quick. There are probably a few more but I haven't found any more. The GT40 classic car is quick and I think may suffer from the quick steering issues of the LMS just not as severe but it's is a very temperamental drive if not fun and daunting when in a race.
Ok a thing about grip and slip in relation to tire simulation. I tend to drive on CS or SH on cars in GT6 and what I noticed is losing grip in GT6 is a very marked experience. I have over driven the tires and started losing the back end and all it took was getting off the car and countersteering a tad and allowing the inertia to straighten the car, in GT5 you had to jostle the steering in order to attempt to save it and it didn't always work because of the weird on/off grip GT5 had at the limit, once you reached the limit all grip was lost and it was anyone's guess when the grip was turned back on after you got off the throttle, some times it was sudden and the car would dart off in an unintended direction. GT6 is way more progressive and you actually feel grip slowly running out and even with the weird ridiculously fast steering(on a pad set to 0) letting the LSD reign in the wheels to get your grip back while steering the car to line it up.
Ok before trying to tune first know how to drive the car a little first, if you can't understand why you're losing control what exactly are you going to tune?
http://www.rac3.info/setup/?l=en
I use this whenever I get a car and put on a custom suspension, strange thing is it was built for GT5, yet it works for GT6's values. These values are just base values riding on how stiff you want your suspension or how soft. Again this is still a game and there could be a lot of things wrong in it, but that's not to say that it doesn't get things correct and it's simply driver who needs to learn to be smoother rather that simply being i/o with power and braking. Take your time and learn to modulate throttle and braking when you can use minute changes mid corner to keep your car planted you'll soon see how you can make the car go faster.