It's simple. To me the driving in GTA V is like getting a Formula 1 and racing it around a circuit like Yas Marina in Abu Dhabi where it's fast flowing and smooth. The only time cars ever really get unsettled is when you clip another car. In GTA IV there are bumps in the road and the kerbs/gutters can also really screw things up if you hit them the wrong way.
The biggest thing I've noticed between GTA IV and GTA V is with GTA IV you have to really muscle the cars around corners and control weight transfer over the rear (unless it's front wheel drive) whereas GTA V basically does everything else and all you have to do is brake, accelerate and steer.
Apparently every car has slick racing tyres, 1000kg of front and rear downforce, coil over suspension and can accelerate as good as any Ferrari, Lambo, Porsche etc.