As seen through most of the TV series - including Next Generation - the Borg are mostly seen with one or two eyepieces. But the eyepieces are not always on the same side of the face for each different Borg. Is there an in-universe explanation for this? Or is it just the way the producers show differences between them?
The entry in the official Star Trek Encyclopaedia states that Borg implants are added to each drone depending on the needs of the collective.
Different eyepieces are seen because the drones will need different sensing capabilities to do their assigned jobs. It makes little sense to outfit a Medical Drone with the ability to target objects at great distance, for example.
Tactical Drones, for example seem to have long-lens type eyepieces on their right whereas Medical Drones appear to have a microscoping eyepiece with multiple lenses. Normal 'labor/maintenance-type' drones seem to have the bog-standard holographic eyepieces that we see in TNG: I, Borg whereas the Borg Queen's eyepiece seems to be wholly internal.
Regarding the side of the head that the device is fitted to, there are a couple of possible reasons:
Out of universe answer
Gil Mosko, makeup artist for TNG, Voyager and First Contact describes the evolution of the eyepieces over time. The side chosen appears to be totally random, as part of an effort to create a "unique feel" for the alien nature of the Borg.
Michael Westmore, Makeup Supervisor for TNG, Voyager and First Contact seems to be suggesting that the eyepieces were styled to fit the headpieces, rather than the other way around;
In universe, we are given just enough technobabble to relate to whatever story elements are needed.
Borg heads-up optical display being shown in Star Trek: Borg - Part 3: The Hunt.
The eyepiece must be significant because even infant Borg are outfitted with them.
There is one Borg who I can think of that has no eye prosthetic at all. Locutus, of the 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, repetetive functions.
Locutus is special, in that he is an 'envoy' of the Borg. Thus he has an unobstructed face to make him as recognizeable 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.