The spacings-based goodnes-of-fit test statistics known from the literature are shown to be asymptotically equivalent to spacings-based Pearson-type statistics. Limit laws will be extended, and the related relative asymptotic efficiencies will be evaluated for new clases of such statistics. New limit laws and the related asymptotic efficiencies will be obtained also for new classes of the Pearson-type statistics based on finite quantizations of observation spaces the sizes of which increase to infinity with the sample size tending fo infinity. The asymptotic efficiencies will be compared and rules for the choice of optimal text statistics will be formulated and experimentally verified.