What is the difference between either-or and dialectic logics?
Perhaps we should be a little more skeptical that both of these logics fits into the same family first.

So, in the eyes of dialectic logic, what is either-or?
Simply, it is in error (if both are true, for me to say 'one is in error' is a direct denial of the dialectic). But the dialectic logic would claim that both ideas of truth are true, even though the disagree. This would deny the definition of truth (for if everything is, then the label is a label of existence, not of meaning).

What about dialectic logic in the sight of either-or?
It's an overgeneralization of the either-or. For example, a group of people are split on an issue. Is it true that the group as an entity believes that both are true? Yes. However, this occurs because it misconstrues the beliefs of the group. Each individual is thinking a particular thing (either good or bad) about the issue. One could argue that a person can thing both things at different points in time. This is precisely my point as to the problems of the dialectic thinking, because it is simply a misunderstanding of the object in question. Inevitably, an either-or immerges from any dialectic when the object is properly framed.

So...could the dialectic demonstrate anything other than the lack of what it is meant to discuss? I don't see how. But the either-or logic manages make sense, both of itself and the perception of dialectic logic. Is the dialectic important to understanding movements (ie generalizations) - undoubtedly. But does this bring its equivalence to being used in a similar way to either-or - undoubtedly not.