A preference is about choice. An opinion is about conclusions/beliefs/facts/etc. I don't see one as a subcategory of the other. Though the words can overlap if you want to have a opinion that your preference is 'better' or 'prettier' or some other quality.
I prefer dogs to cats. It is my opinion that dogs are friendlier than cats. Two different words that mean two different things. Substitute the word "prefer" for "like" and substitute "opinion," for "judgement." Does that help?
As far as I can see, an opinion can be correct or incorrect, whereas a preference simply is. On the other hand, I can see how the boundary can be blurry, because something like "George R R Martin's writing is too wordy" seems to be a opinion - true or false - but at heart it's really just a preference about how wordy you like a writer to be.
