Stomatal conductance schemes that optimize with respect to photosynthetic and hydraulic functions have been proposed to address biases in land-surface model (LSM) simulations during drought. However, systematic evaluations of both optimality-based and alternative empirical formulations for coupling carbon and water fluxes are lacking. Here, we embed 12 empirical and optimization approaches within a LSM framework. We use theoretical model experiments to explore parameter identifiability and understand how model behaviors differ in response to abiotic changes. We also evaluate the models against leaf-level observations of gas-exchange and hydraulic variables, from xeric to wet forest/woody species spanning a mean annual precipitation range of 361-3,286 mm yr(-1). We find that models differ in how easily parameterized they are, due to: (a) poorly constrained optimality criteria (i.e., resulting in multiple solutions), (b) low influence parameters, (c) sensitivities to environmental drivers. In both the idealized experiments and compared to observations, sensitivities to variability in environmental drivers do not agree among models. Marked differences arise in sensitivities to soil moisture (soil water potential) and vapor pressure deficit. For example, stomatal closure rates at high vapor pressure deficit range between -45% and +70% of those observed. Although over half the new generation of stomatal schemes perform to a similar standard compared to observations of leaf-gas exchange, two models do so through large biases in simulated leaf water potential (up to 11 MPa). Our results provide guidance for LSM development, by highlighting key areas in need for additional experimentation and theory, and by constraining currently viable stomatal hypotheses.