First, Fairy Fire does not provide a strong area of light. I see Fairy Fire as magically highlighting something, sort of like using a yellow marker on text in a book. The marker makes something stand out. But it doesn't make the text easier to read if you're sitting in the dark. And it doesn't help much if the book is in Braille.
I also rule that Fairy Fire does not help someone who is blind(ed). If someone can't see, making a target "sparkle" isn't going to give advantage, unless the DM decides that the sparkle is also audible, hissing and popping like static electricity or something.
I rule that Darkness does not dispell it because FF is not just illumination of an area centered on a target. Likewise, Darkness does not dispell the cantrip Produce Flame. That little bit of magical fire is still there and could be thrown (at disadvantage), but it just can't be seen while in the magical darkness.