Electro-osmotic flow (EOF) plays a crucial role in the functioning of devices in micro- and nanofluidics. In order to optimize the operation of a device, polymer coatings are often used to control EOF. Our simulations examine the case of grafted, charged polymer coatings for this purpose and compare the electro-osmotic flow mobility produced by a given polymer coating to the free-flow electrophoretic mobility of the polymers making up that coating. The simulation results are compared to both experimental data and theoretical predictions. One particularly interesting result is that the direction of the EOF reverses well before the net charge of the interface changes sign.