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Accuracy measures for parameter estimates represent a tricky issue in nonlinear models. Practitioners often use the separate marginal confidence intervals for each parameter. However, these can be extremely misleading due to the curvature of the parameter space of the nonlinear model. For low parameter dimensions, routines for evaluating approximate simultaneous confidence regions are available in the most common software programs, but the degree of accuracy also depends on the intrinsic nonlinearity of the model. In this paper, the accuracy of the marginal confidence intervals, Hartley's exact simultaneous confidence region (sCR), and the most widespread approximate sCR are compared via both real data and simulations, for discrete time diffusion models in the class of nonlinear regression models.