I'm pretty sure that this is normal. The jpg has the in-camera color space and gamma applied before you see it rendered. The nef file is rendered exactly as shot without any in-camera processing. The nef will look particularly bright if you have "exposed to the right" on your camera histogram.
After some image manipulation in Lightroom's Develop module the nef file should look more as you are expecting. See if this helps.
Good luck,
Stan