This paper addresses the interfacing between quantum and classical processors, which plays a crucial role in quantum-classical hybrid algorithms. Specifically, we compare and analyze the "classical shadow" method, which efficiently extracts essential classical information from a quantum state, with the "quantum footage" method, which is a direct quantum measurement, to quantitatively identify the efficiency bounds of each method. For observables expressed as linear combinations of poly matrices, the classical shadow method excels when the number of observables is large and the poly weights are small. For observables in the form of large Hermitian sparse matrices, the classical shadow method is advantageous when the number of observables, the matrix sparsity, and the number of qubits fall within specific ranges. Key parameters such as the number of qubits ($n$), the number of observables ($M$), the sparsity ($k$), the poly weights ($w$), the accuracy requirement ($\epsilon$), and the failure tolerance ($\delta$) influence this behavior. Furthermore, we compare the resource consumption of the two methods on different types of quantum computers and identify the break-even point at which the classical shadow method is more efficient, which varies depending on the hardware. In conclusion, this paper presents a novel method for quantitatively designing an optimal hybrid quantum-classical tomography strategy, providing practical insights for selecting the most appropriate quantum measurement method for real-world applications.
