The morphology of liquids confined to linear micrometer-sized grooves of triangular and rectangular cross section is studied for different substrate wettabilities. Depending on the wettability and exact geometry, either droplike morphologies or elongated liquid filaments represent the generic equilibrium structures on the substrate. Upon changing the apparent contact angle of aqueous drops by electrowetting, we are able to trigger the transition between elongated filaments and droplets. In the case of rectangular grooves, this transition allows us to advance liquid reversibly into the grooves while crossing a certain threshold contact angle. In triangular grooves, however, these elongated filaments undergo a dynamic instability when the contact angle returns to a value above the filling threshold. The different filling and drainage behavior is explained by specific aspects of the triangular and rectangular groove geometry.