I think both books are outstanding, and more complementary than rivals. In fact, I use both. Nevertheless, there are some differences.
Columbia's big dimensions and weight (8.9 pounds/4 kg) make almost necessary to read it on a desk. Britannica Concise (BCE) is 6.7 pounds/3 kg and smaller.
Both utilize an extremely small font size. Columbia contains 6.5 million words. BCE "only" 2.6.
Britannica C has over 2000 photographs, maps, tables, drawings, color illustrations; nations flags ... In Columbia, illustrations are sparse, limited to about 500 black-and-white line drawings.
Columbia's 6th edition stopped in 1999. BCE is of April 2003 and is edited every year in spring, but I don't know if they are going to update it or not.
Britannica Concise has articles like Super Bowl, Viagra, Coca-Cola, Big Stick Policy, Mother's Day and Father's Day ... that don't exist in Columbia.
Quantity does not always mean Quality. B Concise seems to be more shrewd, witty and, by the way, less subjective. For instance, Columbia's article Homosexuality concludes in this way: "But AIDS (.....) also sparked moralistic reactions; some felt, for example, that it represented a form of judgment on homosexuality". BCE's same article is shorter, but neutral, and does not say such a thing.
As I said before, both books are outstanding and complementary.