Spade bits are much messier than Forstner bits, which drill very clean, neat holes.
Forstner bits are also available in much larger diameters than spade bits.
Additionally, Forstner bits can be used to drill into surfaces at an angle. This is not easily done with a spade bit, as a lot of strength is required to hold the bit in place and prevent it from going off course due to its flat shape.
Spade bits bore holes much more quickly than Forstner bits, though, making them better suited to jobs where a lot of holes need to be bored in a short space of time, and where neatness is not an issue.