As, I suspect, with most, my previous exposure to Frances Hodgson Burnett was through The Secret Garden, A Little Princess, and The Lost Prince. Those books are better.
A Fair Barbarian is a harmless and mildly entertaining shift from those child-oriented books to more a young adult's realm. It's pleasantly reminiscent of Jane Austen, though less complex.
The book's strength is the characters, who are interesting and moderately likeable. However, despite a fair-size crew of young men and women looking to fall in love with each other, there's no strong resolution; the ending comes disappointingly ex machina, and the story simply stops.
Recommended for Burnett fans, and pleasant but not compelling for others.