In-Universe answer
------------------

The entry in the [official Star Trek Encyclopaedia][1] 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.

![enter image description here][2]

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][3] seems to be wholly internal.

![enter image description here][4]

Regarding the ***side*** of the head that the device is fitted to, there are a couple of possible reasons:

 - To match the side that the prosthetic arm will be fitted.
 - As twinned pairs (Tactical borg will often walk with a "left-eye" and a "right-eye" [together][5] for example)
 - As @Einer says, if someone has a pre-existing deficiency in one eye, it's reasonable to presume the Borg will replace that eye as a priority
 - **Handedness** seems to be hard-wired into human (and alien) brains. It makes sense not to fight against an *existing* predisposition when there's a completely free choice.

Out of universe answer
---------------

Gil Mosko, makeup artist for TNG, Voyager and First Contact describes the [evolution of the eyepieces][6] 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.

> **Brandon:** *What was it like working on the Borg makeup "upgrades" for
> Star Trek: First Contact and then carrying those over for Star Trek:
> Voyager? Specifically, can you give us any insight into the process of
> enhancing the look of the TV Borg for their big screen debut?*
> 
> **Gil:** *The Borg had been relatively standardized by the time they were
> used in one of the films. Like any television to big screen makeup, we
> had to be more careful about details. The painting of the background
> became an airbrush process beginning with an off-white background. It
> then had beige and taupe air brushed in a mottled pattern. Every hose
> that connected to skin had a foam transition. These looked almost like
> bullet hits, and then the tubing was glued to the inside circle. **Our
> use of “mechanical” looking parts became more flamboyant. We were even
> provided with the centers of electronic wristwatches that would have
> moving elements inside them.***

Michael Westmore, Makeup Supervisor for TNG, Voyager and First Contact seems to be [suggesting][7] that the eyepieces were styled to fit the headpieces, rather than the other way around;

> **How has the Borg make-up evolved?**
> 
> I had to figure out what to do with the hands and the head.
> **They had these helmet-like devices on that had openings in them, and
> they could be scarred. It was a very quick make-up that way, the
> helmets were all pre-painted, even if there was a hole and an opening,**
> that area could have been pre-painted with the same colour make-up
> that we'd use on their face.
> 
> It was just a matter of putting a foundation on their face, air
> brushing some shadows into it, slipping the helmets onto them and **just
> gluing down around the edges and putting on the eye piece, of which
> the original eye pieces didn't have any mechanical workings or lights
> to them at all.**


  [1]: http://en.memory-alpha.org/wiki/Star_Trek_Encyclopedia
  [2]: https://i.sstatic.net/8QO6z.png
  [3]: http://i127.photobucket.com/albums/p154/kevoris/bqs3.jpg
  [4]: https://i.sstatic.net/wgSND.jpg
  [5]: http://cdn.smosh.com/sites/default/files/ftpuploads/bloguploads/0813/the-borg-star-trek.jpg
  [6]: http://trekinitiative.wikia.com/wiki/User_blog:Brandon_Rhea/Interview_with_Gil_Mosko
  [7]: http://www.bbc.co.uk/cult/st/interviews/westmore/page8.shtml