Partial F corresponding to a stimulus/contrast indicates how statistically significant this stimulus/contrast accounts for the whole variation in the output signal. Full Fstatistic tests whether one of the regressors (or stimuli) is statistically significant, that is, is the signal at a voxel simply just some noise OR activation due to ANY of the stimuli?
So if you want to check if there is any activation at a voxel, use full F as your thresholding quantity; otherwise if you want to know one condition-specific activation or contrast, go with the corresponding partial F.
Gang