Regime channels are important for stable canal design and to determine river response to environmental changes, e.g., due to the construction of a dam, land use change, and climate shifts. A plethora of methods is available describing the hydraulic geometry of alluvial rivers in the regime. However, comparison of these methods using the same set of data seems lacking. In this study, we evaluate and compare four different extremal hypothesis-based regime methods, namely minimization of Froude number (MFN), maximum entropy and minimum energy dissipation rate (ME and MEDR), maximum flow efficiency (MFE), and Millar's method, by dividing regime channel data into sand and gravel beds. The results show that for sand bed channels MFN gives a very high accuracy of prediction for regime channel width and depth. For gravel bed channels we find that MFN and 'ME and MEDR' give a very high accuracy of prediction for width and depth. Therefore the notion that extremal hypotheses which do not contain bank stability criteria are inappropriate for use is shown false as both MFN and 'ME and MEDR' lack bank stability criteria. Also, we find that bank vegetation has significant influence in the prediction of hydraulic geometry by MFN and 'ME and MEDR'.