We analyse the competition of antiferromagnetism and superconductivity in the two -dimensional Hubbard model at moderate coupling. By using the functional renormalization group in its fully dynamical implementation, we compute the flow of the vertex function and of the magnetic and superconducting order parameters. In spite of strong frequency dependences of the effective interations and the pairing gap, we confirm important physical results from previous static functional renormalization group calculations. The magnetic critical temperature is interpreted as the onset of pseudogap behavior. Computing the Kosterlitz-Thouless temperature from the superfluid phase stiffness, we obtain a superconducting dome in the Temperature-doping phase diagram centered around 15 percent hole doping.