There is one Borg who I can think of that has no eye prosthetic at all: Locutus of Borg.
This suggests that the addition of such a prosthetic is a function of the Borg's purpose in the collective. Most Borg are drones, designed to serve simple, repetitive functions.
Locutus is special, in that he is an 'envoy' of the Borg. Thus he has an unobstructed face to make him as recognizable as possible.
This at least answers why certain borg (Locutus) have no eye prosthetic. And I think the other answers give good reasons for why other Borg might have eye prosthetics on either side.
