Future planetary exploration missions demand high-performance, fault-tolerant computing to enable autonomous Guidance, Navigation, and Control (GNC) and Lander Vision System (LVS) operations during Entry, Descent, and Landing (EDL). This paper evaluates the deployment of GNC and LVS algorithms on next-generation multi-core processors--HPSC, Snapdragon VOXL2, and AMD Xilinx Versal--demonstrating up to 15x speedup for LVS image processing and over 250x speedup for Guidance for Fuel-Optimal Large Divert (GFOLD) trajectory optimization compared to legacy spaceflight hardware. To ensure computational reliability, we present ARBITER (Asynchronous Redundant Behavior Inspection for Trusted Execution and Recovery), a Multi-Core Voting (MV) mechanism that performs real-time fault detection and correction across redundant cores. ARBITER is validated in both static optimization tasks (GFOLD) and dynamic closed-loop control (Attitude Control System). A fault injection study further identifies the gradient computation stage in GFOLD as the most sensitive to bit-level errors, motivating selective protection strategies and vector-based output arbitration. This work establishes a scalable and energy-efficient architecture for future missions, including Mars Sample Return, Enceladus Orbilander, and Ceres Sample Return, where onboard autonomy, low latency, and fault resilience are critical.