Neutral applies the lowest possible level of contrast and saturation - even less than standard. So in an image with a large dynamic range, neutral may give you a bit more space to assess adjustments to exposure.
Generally I'm using Standard these days. I have found that higher contrast levels in Vivid and Landscape picture controls are also more likely to generate excessive highlights and shadows.
As the others have indicated, the RAW image data is the same with all of these options. But the embedded JPEG is different, and you do have a great deal of latitude to process a neutral file with minimal contrast or alternative contrast in Capture NX2 or other tools.
In practice, I tend to make adjustments in post processing if I have an image that needs an exception. So I might move from Standard to Neutral and then only apply contrast as needed. I might even make decisions about applying Contrast differently to luminance vs. chromninance channels.