Burberry is older than Barbour. Burberry was founded in 1856 by Thomas Burberry, whereas Barbour was founded later in 1894 by John Barbour.
While Barbour is not older, it is a long-standing British heritage brand known for its iconic waxed cotton jackets. Burberry is renowned for inventing the trench coat and pioneering breathable fabrics like gabardine in the 19th century.