A display may have an array of light-emitting diode pixels or pixels containing portions of a liquid crystal layer to which electric fields are applied using electrodes. A pixel with a light-emitting diode may have a drive transistor coupled in series with the light-emitting diode. A storage capacitor may be coupled to a gate of the drive transistor. A pixel with a liquid crystal portion may have a storage capacitor coupled to a given one of the electrodes in that pixel. Switching circuitry in each pixel may be used to load data from a data line into the storage capacitor of the pixel. The switching circuitry may include a semiconducting-oxide transistor coupled to an associated data line and a series-connected silicon transistor that is coupled to the storage capacitor.