Trevor, On the ULN2803, the com pin connects to the  positive 12 vdc supply and the driver in the chip connects the load connected to the output pin to ground.  The common of all of your magnets is connected to 12vdc rather then ground. On the UDN 2981,  the common or ground pin connects to ground and the 12vdc supply connects to VS on the chip. In this case, the UDN is switching DC positive voltage to the high side of the magnets.  One side of all of the magnets are connected together and to