Having played all of these games recently (still playing both NFS games today, it really does depend on what you like in a racing game.
Shift 2 is my personal favorite as it has a blend of simulation and arcade elements, and it has a great car list and some fantastic tracks (Nurburgring Nordschliefe, Mount Panorama, Road America and Silverstone to name a few). It is also incredibly exciting to play after playing GT5 as the AI is unpredictable (though sometimes frustrating), the cars really feel alive both visually and physically and the sense of speed is brilliant.
However, the controls can take getting used to, but they are massively improved by altering the control settings.
If you are looking for an exciting sim/arcade racer, then this is definitely the one for you.
NFS most wanted is also very good (and is now free for PS+ subscribers 👍), but is also very arcadey, in that cars have to be drifted round corners to go at their fastest, as you do in GRID 2. The car list is mainly based around supercars, though there are one or two hot hatches and even a Ford pickup truck. Graphically though, this game is very pretty and I haven't noticed any dramatic frame rate drops when there is a lot happening on screen.
But I found that this game can quickly become boring as you often just find yourself repeating races but just in a different car, and the lack of camera choices can be off putting for some, as there is only a bumper camera and 3rd person camera

.
If you like supercars, open worlds and cop chases, then this should be the obvious choice.
Now if i'm honest, GRID2 was a big disappointment for me as the title is was misleading. GRID 1 was great as it involved a lot of circuit racing, with the odd street race thrown in. But GRID2 is the polar opposite, and perhaps it's just me but the physics are more arcadey than before which i'm not a fan of. If I had to find a positive, then I suppose the 'objective' is fairly original, in that you have to build up a fanbase to promote a racing series. Also, as its the more recent game, there are newer cars, such as the Aston Martin ONE-77 and the BAC Mono
I suppose if you like Arcade racers in the city, then you should choose this one.