This paper compares a newly proposed method, namely the junction-point water stage prediction and correction (JPWSPC) method, for gradually varied subcritical flow simulation in general open-channel networks with conventional three-phase algorithms. Emphasis is on their difference in backwater effect treatment and efficiency. When the two classes of algorithms are implemented, the Saint-Venant equations are discretized using the Preissmann scheme and the resulting nonlinear equation system is solved using the Newton-Raphson method. The comparison shows that the two classes of methods are applicable in general networks, that, furthermore, the JPWSPC method saves computer memory and computation time by avoiding to establish and solve the global matrix without increasing the required number of iterations per time step, and that the advantage of the JPWSPC method over the three-phase algorithms increases with increase of the number of junction points.