Offhand I wouldn't think that there is a left/right-eyedness that is at the same level as left-right-handedness. The hands are designed to work separately, but the eyes almost always work together e.g., for some portion of depth perception and focus and such. I recall that for the pupil reflex, both eyes are normally synched, and this is a standard test to check for normal brain activity. So I guess that's an indication that the brain is fundamentally wired to interpret the optical signals in a binocular way.
Moreover, I don't know if the visual cortex is truly divided between the left and right hemispheres as much as many other faculties; I seem to recall that vision itself is well centered even if perception and analysis are not, so that might also be relevant.
Now, as for how you interpret or analyze things, sure, that could be 'handed.' People do interpret scenes in different ways, e.g. creatively or analytically or both. I recall this visual test which is supposed to determine whether you are left or right brained:
In case you didn't notice it, there is a man's face among the coffee beans, and the speed with which people would recognize that is supposedly related to creative/analytical abilities. I thought this was nonsense when I read about it but then I did it and actually saw the face immediately, whereas some friends didn't even after 10 seconds. And I am indeed very analytical. So who knows....
Anyway, I don't think that creative/analytical ability overtly manifests itself in left or right-eyedness: tests such as the one above probably yield the same results regardles of which eye you use to do them. Unless of course there is a
physical difference between the eyes, i.e. impairment on one side!
I think the difference between colour and b&w vision is very interesting; I am quite convinced that we have different ways of perceiving/interpreting colour or b&w scenes, and that is of course wrapped up in the way the rods and cones work.