Act as a Quantum Information Theorist. Compare and contrast the Quantum Approximate Optimization Algorithm (QAOA) and Grover's Search algorithm when applied to the Max-Cut problem on a specific graph class (e.g., 3-regular graphs). Analyze the theoretical query complexity and circuit depth requirements for both algorithms. Discuss the impact of noise (decoherence and gate errors) in current NISQ (Noisy Intermediate-Scale Quantum) devices on the performance of these algorithms. Conclude which approach offers better near-term viability for practical problem-solving and provide mathematical justification for your stance.