Crows -v- Magpies

Having watched over many years the nests of our garden birds being raided by a pair of magpies that nest nearby (not sure if they are the same pair), this year a pair of crows have nested for the first time in one of our avenue trees nearby. The magpies are very unhappy and have tried to attack the crows. Would the crows and magpies predate each others nests? Is it likely that the crows will also raid smaller birds' nests or can we hope that they might deter the magpies?