By implementing a unique magneto-optical system with ultrafast magnetic-field ramping-rate capability (up to 3 kT/s), we have been able to routinely generate and image dendritic flux instabilities in YBa2Cu3O7-x films. In the present work we study the effect of the film thickness on the dendritic instability. Dendritic avalanches in 50 - 600 nm thick films were magneto-optically imaged at 7 K, after ramping the magnetic field from zero to 60 mT at different rates. The data reveal a remarkable change in flux morphologies between the thin and the thicker films. While the former (50-250 nm) display well-developed dendritic patterns, the latter (350-600 nm) exhibit few avalanches with favored branch directions parallel to the film's edges. Several possible explanations for this behavior are discussed.