Larger formats exist mainly to increase the level of detail in the photographs produced. This was certainly true in the film era as film resolution was pretty much fixed (per unit area) but a larger negative could always produce more detailed prints. It is also largely true in the digital age as the highest megapixel sensors available are all larger than 35mm.
Shooting in low light leads to a lack of detail due to the noise that results from amplifying a weak signal. It therefore does not make sense to use a medium format digital camera for low light work as you wont get an appreciable gain in resolution. Thus medium format sensors are optimised for use at low ISO.
You wouldn't get many gains from the larger pixel size made possible for a larger sensor either, as medium format lenses are typically slower (smaller max aperture) in order to save weight (and again due to the use of medium format for detailed work, fast lenses produce less detail). f/2.8 is rare, f/2.0 lenses even more so.