Unfortunately, I played the PS3 version which is good news for you because the 360 version can only be better.
The game is playable with the default settings and a gamepad to begin with, cars feel twitchy and light at high speeds but like I said, you can make them behave however you want.
Playing around with the deadzones and sensitivity will make a huge difference and I've heard that the 360 version has less or no input lag whatsoever, which is something you can get rid off if you use Game Mode on your TV and it'll work for all your games, specially shooters.
Like FM4's Normal Steering, cars tend to be stable at low speeds and easy to correct, at high speeds though, they do tend wobble a bit but you can fix that by increasing the Caster angle and reducing the Steering lock which are tuning options available on all cars, you don't need to purchase any parts to adjust this stuff.
Also, for some reason, the tyre pressure is set too high on default for all cars which makes them very tail-happy. Adjusting that alone will make a huge difference.
The game is just so much fun, do I need to mention that you can Works convert a.k.a. Race Mod any car in the game? Wonder how a Alfa 8C race car would look and sound like?
Sounds are definitely not as pristine as FM4, they're raw and in some cases a bit fake but they're incredibly immersive. You not only hear engine and exhaust notes but the whole body of the car just being murdered by the G-forces, you can hear the suspension working, the brakes locking up aside from the tyre screeching that comes with it.
Really, this game is easily the next best thing after Forza and Gran Turismo, it has what the other 2 lack, the thrill of racing, sometimes you might even feel fear as you fly through the Ring in a Koenigsegg CCX.
The AI is mad like FM4's AI but the difference is that they can keep up with the best of your paces and they will overtake you if you're sluggish through a corner, they just don't care.
Something that a lot people need to get off of their minds is that Shift and Shift 2 are the same, Shift 1 was like Grid but with input lag, Shift 2 is closer to FM and GT than Grid.