Experiments on the spatial and temporal structure of the breakdown process of sinusoidal- and pulsed-operated dielectric barrier microdischarges (MDs) are compared. Three different waveforms are considered: a sinusoidal waveform at 20 kHz and pulsed-bipolar and unipolar-voltage profiles at 10 kHz with varying duty cycles (asymmetric pulse). Electrical data and simultaneous streak and iCCD images of individual MDs in dielectric barrier discharges (DBDs) with 1 mm gap in a gas mixture of 0.1 vol% O2 in N2 at atmospheric pressure are recorded. For sinusoidal-operated DBDs there are no significant differences between the MDs at positive and negative half-periods. Sinusoidal operation corresponds to pulsed-bipolar operation with symmetrical pulses, but with lower streamer velocities and different spatio-temporal emission distribution. The development of pulsed-driven MDs is determined by the voltage between both electrodes and not by the polarity of the driven electrode, resulting in nearly the same behavior of bipolar- and unipolar-pulsed-driven MDs. DBDs operated with asymmetric pulses show a significant difference in the spatial structure and in the temporal behavior between the rising and falling slopes of the high voltage pulse.