Two distinct nonlinear programming formulations are investigated for ODE optimal control problems with pointwise state and control constraints. The rst formulation treats the differential equations of state as an equality constrain in the conventional manner. The second formulation employs a different equality constrain entailing the integrated state transition map. Related convergence rate estimates are developed for augmented gradient projection methods and discrete-time approximations to a large representative class of ODE control problems. In the rst formulation, the rate estimates are mesh-dependent, and the predicted number of inner loop gradient projection iterations needed to achieve a fixed small deviation from the optimal value of the augmented Lagrangian is inversely proportional to the square of the mesh width. In the second formulation, the convergence rates and predicted iteration counts are mesh-invariant. The computational costs-per-iteration in the two formulations are comparable. These estimates elucidate previously published numerical experiments with augmented gradient projection methods and constrained regulator problems.