If we consider an "eye" to be a single biological structure which has the purpose of encoding an image of the world such that its owner can perceive and act within that world based on the image, then this can cover a broad range of sensory organs.
There can be good reasons why an organism - even one that relies heavily on vision - might evolve to have only one "eye" rather than two or more, provided that the organism has the right type of eye.
If we consider the human eye, it has a single lens that focuses light onto an area of photosensitive cells, giving two-dimensional perception.
If we consider an insect's compound eye it is made up of many ommatidia, each of which represents one or seven pixels in the insect's field of view.
Now consider something in between these two types of eye. If we have a compound eye made up of many subunits that are more like a human eye - each subunit having a lens that focuses light onto an area containing many photosensitive cells, then each subunit would form is own image with a fair amount of detail. By combining the images obtained from all the adjacent subunits, each of which would be pointing in a slightly different direction, and is also slightly offset from its neighbours, we get an optical array that is similar to that found in a light-field camera.
This means that unlike both human and insect eyes, depth perception does not require two or more structures, but only one. By placing an array of eye subunits on part of the organism's body, potentially forming a spherical structure, the organism could gain a 360° 3D view of its surroundings that is in-focus at any range. The organism could house processing structures within the eye's structure, and pass a processed image to its brain.
While made up of multiple subunits, each of which could be an eye, the structure operates as a whole. This form of eye has the advantage that the organism has equally good vision in all directions at all distances simultaneously, and gains a true 3D concept of its environment. Unlike human eyes, there is no delay for focusing or tracking. This would be of advantage to a creature that could be attacked from any direction by quick airborne and land-based enemies.
However, this form of light-field eye would most likely suffer from the problem that it has a lower resolution, sacrificing perception of fine detail for broad coverage at any range, unless the organism has a particularly large portion of its brain devoted to visual processing.
Now, to address the original question: Would it be more advantageous to have only one of these light-field eyes, or more advantageous to have more than one?
The answer would be that under most circumstances it would be advantageous to have only one. Each light-field eye would require a significant amount of processing power, and each spherical light-field eye could have a field of view that, if placed at the top of the organism's body, would cover the organism's entire surroundings with the exception of into the structure supporting the eye. If there were two, they would require additional processing structures with their associated metabolic costs, they could conceivable obstruct each-other's field of view, and they would be unlikely to provide much advantage, as each alone produces a 3D image that is in-focus at any range.
Under such circumstances, an organism with only one 360° light-field eye that covers all potential avenues of attack would have a metabolic advantage over an organism with more than one, hence favouring cyclopia. There is the issue that the eye would lack redundancy, however if the organism's predators are a sufficient threat that being captured is typically fatal, this would tend to favour the system with the lowest metabolic cost. Additionally, since the light-field eye is made up of many subunits, some subunits could be lost without greatly degrading the acuity of the eye as a whole, unless several adjacent subunits were lost.
An evolved light-field eye would be quite similar to the Lytro Immerge camera, though could cover the area directly overhead in a way that the Immerge doesn't appear to do.