We study the competition between sedimentation, gelation, and liquid crystal formation in suspensions of colloidal gibbsite platelets of five different sizes at three ionic strengths. For large particles (with diameters of 350, 420, and 570 nm) sedimentation is initially the most important factor determining the macroscopic behavior. Only after the main part of the sample has sedimented in an amorphous phase, phase separation takes place. For the smallest particles (diameter 210 and 270 nm), it is the other way around: fast (within one week) phase separation or gelation takes place, after which sedimentation determines the final macroscopic appearance. We distinguish six different scenarios within this two-fold scheme and interpret these on the basis of the previously obtained phase diagram of colloidal gibbsite platelets.