First seen in Despicable Me, what, aside from binocular vision, eye count, and goggle style, are the differences between 1 eyed and 2 eyed minions? Image courtesy of http://ihdwallpapers.com/
There is no official information on it, but I do have a theory: identification
As per the Despicable Me Wikia page on Minions (emphasis mine):
Minions are a similar size and shape, but have unique features to tell them apart, such as height, number of eyes, roundness or secondary features such as hair, eye/pupil size or clothing.
From this, it seems that there is no difference between single-eye and two-eye minions. The number of eyes is simply one of the varying features of the minions used to differentiate them, you know, so you can tell if it's Steve:
who, to me at least, seem identical in all other respects!