We investigate the yielding and transition to flow of different colloidal glasses. Using a single model system, a binary mixture of colloidal hard spheres with different compositions and size ratios, we study single, double and asymmetric glasses, which differ in the degree of mobility of the small particles and the caging mechanisms of the large spheres. The rheological response following either a step to a constant shear rate or to a constant stress (creep) is measured and the two responses are quantitatively compared. Although the same steady state of flow is observed at long times, the transient responses in strain- and stress-controlled experiments differ significantly. To achieve yielding and a steady state of flow, less time and less energy input is required if a constant strain rate is applied. Moreover, larger strain rates or stresses result in faster yielding and flow, but require more total energy input. If a constant strain rate is applied, yielding and the transition to flow depend on the properties of the glass state, while much smaller differences are observed if a constant stress is applied. (C) 2017 The Society of Rheology.