This paper introduces a quantitative generalization of the ``more capable'' comparison of broadcast channels, which is termed ``more capable with advantage''. Some basic properties are demonstrated (including tensorization on product channels), and a characterisation is given for the cases of Binary Symmetric Channel (BSC) and Binary Erasure Channel (BEC). It is then applied to two problems. First, a list decoding bound on the BSC is given that applies to transitive codes that achieve capacity on the BEC. Second, new lower bounds on entropy rates of binary hidden Markov processes are derived.