Large Full frame (35.9 x 24 mm) sensor Large sensors provide shallower depth of field and a nice blurry background for your portrait shots.
Very High Resolution Sensor: 24.0MP Nikon D750's 24.0MP sensor will provide larger room for cropping, and you will be able print your portrait shots larger with more fine detail.
Optical Built-in Viewfinder During a portrait shoot, using a viewfinder allows the photographer to stabilize the camera and reduce the camera shake since it is closer to the body. Besides, it comes handy where LCD screens are very hard to read under bright sunlight.
Good Ergonomics&Handling Good handling and existence of well placed physical controls on the camera body is very important during portrait shooting. It is faster and more intuitive to change the camera settings with dedicated buttons and knobs instead delving into the menus on the LCD.
No Image Stabilization Due to the lack of sensor based Image stabilization, Nikon D750 users have to rely on lenses with optical IS in order to maximize the sharpness of their handheld portrait shots. Currently there are native Nikon F mount lenses with Image Stabilization for Nikon D750.