The sediment transport capacity in subaerial and subglacial channels depends on shear stress at the channel bed, influenced by water velocity and geometry. Subaerial channels accommodate discharge variations through flow depth, width, and velocity changes. In contrast, subglacial channels, confined by overlying ice, grow slowly due to frictional heating, so sudden discharge changes primarily affect velocity. This study presents formulations for sediment transport capacity in both channel types and applies models to hydrographs from an Alpine glacier and the Greenland Ice Sheet. Results show that sediment transport capacity often peaks before maximum discharge, causing hysteresis that decouples sediment transport and water flow in subglacial systems. Subglacial channels can sustain high sediment transport across various discharge levels. Reducing discharge variability diminishes hysteresis, sometimes producing sediment-water discharge relationships resembling subaerial systems. Additional experiments highlight the non-linear behavior of subglacial sediment transport, resulting in greater variability. However, subglacial transport capacity variations approach subaerial ones when subglacial discharge changes in equilibrium with channel size. This work offers a framework for comparing sediment transport capacity in glacial and subglacial systems. The results improve interpretations of sediment discharge records in glacierized catchments influenced by different hydro-climatic conditions and contribute to predicting sediment fluxes under changing climatic and hydrological regimes.