Connecting multiple smaller qubit modules by generating high-fidelity entanglement is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer depends on the quality and rate of entanglement generation. However, identifying optimal architectures and entanglement generation protocols remains an open question. How can modular quantum architectures be designed to achieve fault tolerance while requiring only feasible entanglement rates and hardware? Focusing on solid-state quantum hardware, we investigate the threshold and logical failure rate of a fully distributed surface code. We consider both emission-based and scattering-based entanglement schemes between the modules to link the performance to the physical hardware and identify the regime for fault tolerance. We compare architectures with one or two data qubits per module. For some entanglement schemes, thresholds nearing the thresholds of non-distributed implementations (~ 0.4%) appear feasible with future parameters minimizing the performance gap between modular and monolithic quantum processors.