It looks to me like lighting is your problem.
According to this the default lighting in 3DS Max is essentially a headlamp (a directional light coming from the viewport), so the faces pointing towards you will appear the brightest.
Your Unity preview has a directional light shining towards the bottom right (I could have said "located in the top left", but remember, a directional light has no position).
As for your Unity scene, it doesn't look like you have lighting at all, hence the flat-shaded look of your model. To solve that, I would start with some simple things and ask: do you have any lights in your scene (point, directional, or spot)?