In terms of the eyes actual abilities and nothing like techniques learned
The Rinnigan works like a camera with linked vision and it is assumed to see some sort of nature chakara; thus one has the potential to learn any nature type of ninjitsu. (AKA great for monitoring and securing an area/learning and defending against ninjitsu)
The Sharingan can process rapid movements, can copy enemy ninjitsu, tiejitsu, and genjitsu, can see the color of chakara, and has an hypnotic ability to suggest movments/control anothers mind. (AKA the best for hand to hand combat)
The Buykugan allows one gain the most information at one time, 360/x-ray/in-depth chrakara network/binocular vision. (AKA Data gathering, coordinating, and trap removal)
this would be the point of each of these eyes