Mechanistic theories of fluvial erosion are essential for quantifying large-scale orogenic denudation. We examine the topographic implications of two leading classes of river erosion model, detachment-limited and transport-limited, in order to identify diagnostic and testable differences between them. Several formulations predict distinctly different longitudinal profile shapes, which are shown to be closely linked to terrain morphology. Of these, some can be rejected on the basis of unrealistic morphology and slope-area scaling. An expression is derived for total drainage basin relief and its apportionment between hillslope and fluvial components. Relief and valley density are found to vary with tectonic forcing in a manner that reflects erosion physics; these properties therefore constitute an additional set of testable predictions. Finally, transient responses to tectonic perturbations are shown to depend strongly on the degree of nonlinearity in the incision process. These findings indicate that given proper constraints, fluvial erosion theories can be tested on the basis of observed topography.