Quantum network applications impose a variety of requirements on entanglement resources in terms of rate, fidelity, latency, and more. The repeaters in the quantum network must combine good methods for entanglement generation, effective entanglement distillation, and smart routing protocols to satisfy these application requirements. In this work, we focus on entanglement distillation in a linear chain of quantum repeaters. While conventional approaches reuse the same distillation scheme over multiple hop lengths after entanglement swaps, we propose a novel adaptive quantum error correction (QEC) scheme that boosts end-to-end metrics. Specifically, depending on the network operating point, we adapt the code used in distillation over successive rounds to monotonically increase the rate while also improving fidelity. We demonstrate the effectiveness of this strategy using three codes, with parameters [[9,1,3]], [[9,2,3]], [[9,3,3]], and a new performance metric, efficiency, that incorporates both overall rate and fidelity. Since the minimum input fidelity for QEC-based distillation is high, we then extend our study to include non-QEC-based purification protocols, specifically DEJMPS since it outperforms others. We compare the performance of end-to-end DEJMPS against adapting from DEJMPS to QEC once DEJMPS improves the initial fidelity to the threshold for QEC. Through a refined efficiency metric, we illuminate the regime where QEC is beneficial. These results provide a detailed outlook for entanglement purification and distillation in first and second generation quantum repeaters.