It is shown that micropillar compression can be used to study the plastic flow behavior of both a hard, brittle cubic Laves phase, NbCo2, and a related monoclinic compound, Nb2Co7, which is known to be softer, but is also brittle and has, so far, only been prepared in a fine-grained form. Flow in the Laves phase occurs at a shear stress of 3.1 GPa on the equation image{111} slip system, consistent with previous observations and estimates from hardness measurement. Micropillar compression and electron microscopy of single crystals of Nb2Co7 indicates that flow takes place parallel to the (001) plane, with equation image and equation image type Burgers vectors, at a critical resolved shear stress between 0.1 and 0.5 GPa. It is shown that this is much less than predicted by hardness measurements, consistent with the idea that the hardness of plastically anisotropic materials is determined by flow on the hardest operating slip system.