Photo Credit: Courtesy of 3DStockPhoto ( image)
As I read the history, 3mm filament was an accident of the supply chain when 3D filament printers were first being developed by hobbyists. There was a product called a "plastic welder" which consisted of a melting device and a source of filler material. This filler was 3mm plastic.
As the techniques and equipment developed, the market for filament grew to a size where it could support companies producing filament specifically for 3D printing. The benefits of 1.75mm filament over 3mm were, IMO, huge -- especially the easier melting and lower force needed by the extruder.
Except for special purposes like pushing soft plastics through Bowden tubes, it seems from the marketplace that 1.75mm filament as completely overtaken 3mm filament.
A possible second-order disadvantage of 1.75mm filament can be water absorption. The surface-to-volume ratio is higher -- there is more surface per unit of the filament through which water vapor can be absorbed. It is important to keep filament dry, and sometimes necessary with both 3mm and 1.75mm to dry the filament in an oven before use.