CO cannot, does not, and should not try to directly compete against those airlines - like most of the "superstar" airlines, SQ and VS have the benefit of highly-protected home bases that can command massive traffic volumes and enviable yields. CO's primary competitiors are other US carriers and second-tier European airlines -- BusinessFirst still holds its own against them.

Now if CO gets meaningful access to LHR, the story shall change, and likely for the better...