The work hardening ability under room temperature compression of ductile Cu47.5Zr47.5Al5 and Cu47Ti33Zr11Ni8Si1 bulk metallic glass-forming alloys has been studied and compared. Both alloys exhibit high fracture strength, distinct work hardening and large plastic strain. Systematic investigations on the microstructural evolution reveal the occurrence of nano-scale heterogeneities, of both structural and chemical nature, which enables multiplication, branching, and restriction of the shear bands, thus controlling the plastic instability of metallic glasses. Phase separation in the liquid state leading to chemical inhomogeneities has been revealed for as-cast Cu47.5Zr47.5Al5 samples. In the case of Cu47Ti33Zr11Ni8Si1, a composite-type microstructure with in-situ formed nano-scale precipitates embedded in a glassy matrix is responsible for the distinct work hardening recorded on the stress-strain curves. The present results support the important role of nano-scale heterogeneities for promoting efficient work hardening in Cu-based metallic glass composites.