Should I capitalise "or" between examples?

Solution 1:

Generally, offering two options, of which only one is meant to be chosen, takes a form like this:

Do you prefer "A" or "B"?

In your example, A = "Eggs, butter and milk are dairy", and B = "Eggs, butter, and milk are dairy", so we'd get:

Do you prefer "Eggs, butter and milk are dairy" or "Eggs, butter, and milk are dairy"?

which is closer to your second version.

However, because the difference here is just a single character, I think the most readable version is to use bullets:

Which do you prefer:

• "Eggs, butter and milk are dairy"; or
• "Eggs, butter, and milk are dairy"