This article deals with discrete-time state-space current controllers for three-phase grid converters equipped with an LCL filter. The integral action in the controller can be implemented either using an integrator or a disturbance observer. The results show that the disturbance-observer-based and integrator-based controllers become mathematically equal if the feedforward gains are selected to be equal, the feedforward zero is placed to cancel the pole originating from the integral action, and the closed-loop poles are placed identically. The equivalent performance in both designs is verified by means of analyses and experiments. The equivalence is also shown for double-frequency current controllers.