We use quantitative hypothesis tests to explore variations in channel substrate, geomorphic setting, and incision processes against changes in unit stream power (w) and shear stress (t) in streams incising soluble and insoluble bedrock: Buckeye Creek (14 km² drainage area) and Greenbrier River (3800 km²), West Virginia. Both streams are incising at £40 m Ma^-1 and transport coarse, insoluble sediment. The streams are incising by quarrying, abrasion, and corrosion. Comparisons in thirteen stream reaches reveal that w and t are 3 to 30 times lower atop soluble versus insoluble bedrock. For constant relative solubility, w and t are higher in reaches that interact more closely with hillslopes. Mean cross section velocities are highest where evidence of abrasion is prominent on insoluble channel elements. Evidence of quarrying is associated with higher values of w and t than evidence of corrosion. By inference, the efficiency of corrosion-driven incision on soluble bedrock translates to minimization of mechanical energy expenditure, as represented as w and t. Incision of insoluble strata presumably requires more mechanical energy expenditure for a similar incision rate. Rapid longitudinal changes in w and t are associated with similarly rapid declines in particle size in an alluvial reach in Buckeye Creek. The alluvial reach may couple reaches with high and low w and t by acting as a coarse sediment sink. Depth has adjusted in the Greenbrier River such that changes in t are of lesser magnitude. As a result, coarse sediment transport may be continuous across soluble and insoluble bedrock. Overall, variations of w and t appear to reflect relative substrate solubility, geomorphic setting, and incision processes.