Both formulas are widely taught and used in modern times. Since both equations reference a single control volume location along the channel, neither address friction factor nor head loss directly, but the change in pressure head may be calculated by combining them with other formulas such as the Darcy–Weisbach equation. The empirical aspect to the  coefficient indirectly addresses friction factor and Reynold's number and is the reason why the Chézy formula remains most accurate in certain conditions, such as river channels with non-uniform channel dimensions. Additionally, both equations are explicitly used with uniform or "steady-state" flow where the hydraulic depth is constant, due to their derivation from the conservation of momentum. In contrast, if the hydraulic conditions fluctuate in open channel flow, they are then described as gradually or rapidly varied flow, and will require further analyses beyond these two formula methods.
As partially full pipes are by definition open channels, so long as they aren't pressurized, the Manning and Chézy formulas may also be used to calculate partially full pipe flow; however, these formulas are intended for uniform and turbulent flow. Many other formulas that have been developed since these two may produce more accurate pipe flow results, such as the Darcy–Weisbach equation or the Hazen–Williams equation, but lack the simplicity of the Manning or Chézy formulas.
Both formulas continue to be broadly taught and are used in open channel and fluid dynamics research. Today, the Manning formula is likely the most globally used formula for open channel uniform flow analysis, due to its simplicity, proven efficacy, and the fact that most open channel studies are concerned with turbulent flow. Chézy's formula is one of the oldest in the field of fluid mechanics, it applies to a wider range of flows than the Manning equation, and its influence continues to this day.