The night mode allows longer exposure time... in essence, it uses an algorithm to reuse light picked up in frame 1 when it starts recording frame 2. This does cause a small amount of motion blur, however their algorithm is very good and the quality aberrations are minimal, if not nonexistant. Also, the night mode seems to enhance the darker light areas more than the bright points. What you end up with is slightly more visible dark areas and the light areas (like streetlamps and headlights) are not brighter at all. The end effect is that the overall brightness is higher and objects like streetlamps are not overrexposed causing the entire footage to be washed out with bright light.
The exposure setting I believe operates like the ISO settings on a traditional digital camera but I may be wrong. In short, if you increase the exposure setting you are causing the camera to increase the brightness on the entire picture whereas nightmode only increases brightness on the dark areas.
I've found that unless you are riding in a semi-well lit area, it's not going to be usable footage. When I night vlog I set exposure to +2 and night mode on. Then, in my software I set the gamma to 1.2 or 1.3 (20-30% increase in gamma brightness). If your software doesn't have gamma settings then increase brightness by 20% and contrast by 5-10%. You should end up with the most clear picture and the brightest possible picture you can get using your drift. Remember, in the end you are talking about a camera with a really tiny sensor in it. My handheld canon camera does FAR better night visibility because the digital sensor has about 10x the surface area of the sensor in the Drift.