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)?
Update: According to your comment, you only have the default ambient light enabled in your scene. Note that ambient light is not the same as diffuse light. Ambient light, in typical lighting models, is a shortcut that accounts for light bouncing off of other surfaces. I won't go into much more detail, so I'll refer you here for more information. Note in that link that the version of the blob lit by ambient light looks flat-shaded, exactly like your model in Unity.
The solution to your problem is pretty straightforward then: add a point, direction, or spot-light to the scene. Your model will then look more like it does in the Unity preview.