Developing a quantitative understanding of the factors that control the rate of river incision into bedrock is critical to studies of landscape evolution and the linkages between climate, erosion, and tectonics. Current models of long-term river network incision differ significantly in their treatment of the role of sediment flux. We analyze the implications of various sediment-flux-dependent incision models for large-scale topography, in an attempt (1) to identify quantifiable and diagnostic differences between models that could be detected from topographic data or from the transient responses of perturbed systems and (2) to explain the apparent ubiquity of mixed bedrock-alluvial channels in active orogens. Although certain forms of the various models can be discarded as inconsistent with morphological data, we find that the relative intrinsic concavity indices of detachment- and transport-limited systems (defined herein) largely dictate whether the various models can be tied to distinctive steady state morphologies. Preliminary data suggest that no such diagnostic differences may exist, and other methods must be developed to test models. Accordingly, we develop and explore differences in the scaling behavior of topographic relief and the extent of detachment- versus transport-limited channels as a function of rock uplift rate that may allow discrimination among various models. Further, we explore potentially diagnostic differences in the rates and patterns of transient channel response to changes in rock uplift rate. In addition to general differences between detachment- and transport-limited systems our analysis identifies an interesting hysteresis in landscape evolution: hybrid channels at the threshold between detachment- and transport-limited conditions are expected to act as detachment-limited systems in response to an increase in rock uplift rate (or base level fall) and as transport-limited systems in response to a decrease in rock uplift rate, especially during postorogenic topographic decline. The analyses presented set the stage for field studies designed to test quantitatively the various river incision models that have been proposed.