The best underwater video camera for night diving would also be the Canon Mark III. Night diving requires the use of specific additions to your camera setup that generally entail attachments to the underwater housing. Ikelite is a top manufacturer of aftermarket housings for the most popular models of cameras and they have one specifically made for the Canon Mark III. Their housings focus on ability to use all the controls without taking your hands from the handles.
They manufacture the Pro-2800 LED video light which is touted as the ultimate in brightness, provides light at a rating of 2800 lumens, and can attach right to the housing. With this combination, not only will you have the best underwater video camera available for night shooting but also it is ideal for any other environment. You cannot go wrong with the Canon Mark III if you get a top-end housing with attachable lights that make shooting at night possible. With the housing described, this camera is even rated for depths of up to two hundred feet.
If you shoot video while night diving and have some special techniques, feel free to share in the comments section below.