For the purpose of estimation of possible inaccuracy in standard discrete dislocation dynamics simulations, we study the motion of interacting dislocations in two regimes: the standard stress control and the total strain control. For demonstration of the difference, we consider two dislocations of opposite signs, gliding in parallel slip planes in a channel of a persistent slip band. Exposed to the applied stress, the dislocations move, bow out, and form a dipole. We investigate the passing stress needed for the dislocations to escape each from other, considering the stress controlled regime and the total strain controlled regime. The motion is described by the mean curvature flow and treated by means of the direct (parametric) method. The results of numerical experiments indicate that the stress control and the total strain control provide upper and lower estimate of the passing stress, respectively, and that these two estimates differ by approximately 10%.