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Effective methods for characterizing the noise in quantum computing devices are essential for programming and debugging circuit performance. Existing approaches vary in the information obtained as well as the amount of quantum and classical resources required, with more information generally requiring more resources. Here we benchmark the characterization methods of gate set tomography, Pauli channel noise reconstruction, and empirical direct characterization for developing models that describe noisy quantum circuit performance on a 27-qubit superconducting transmon device. We evaluate these models by comparing the accuracy of noisy circuit simulations with the corresponding experimental observations. We find that the agreement of noise model to experiment does not correlate with the information gained by characterization and that the underlying circuit strongly influences the best choice of characterization approach. Empirical direct characterization scales best of the methods we tested and produced the most accurate characterizations across our benchmarks.