Continual post-training (CPT) is a popular and effective technique for adapting foundation models like multimodal large language models to specific and ever-evolving downstream tasks. While existing research has primarily concentrated on methods like data replay, model expansion, or parameter regularization, the fundamental role of the learning paradigm within CPT remains largely unexplored. This paper presents a comparative analysis of two core post-training paradigms: supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT), investigating their respective impacts on knowledge retention during CPT. Our experiments are conducted on a benchmark comprising seven diverse multimodal tasks, utilizing Qwen2.5-VL-7B-Instruct as the base model for continual post-training. The investigation yields two significant findings: (1) When continuously learning on downstream tasks, SFT leads to catastrophic forgetting of previously learned tasks. In contrast, RFT inherently preserves prior knowledge and achieve performance comparable to multi-task training. (2) RFT successfully protects and even enhances the model's general knowledge on standard benchmarks (e.g., MMMU and MMLU-Pro). Conversely, SFT degrades general model capabilities severely. Further analysis reveals that this stability is not primarily due to explicit mechanisms like KL penalty or chain-of-thought reasoning. Instead, we identify an implicit regularization mechanism inherent to RFT as a key contributing factor. Our theoretical analysis suggests that RFT's gradient updates are naturally scaled by the reward variance, acting as a data-dependent regularizer that inherently protects previously acquired knowledge. Finally, we propose a rollout-based instance filtering algorithm to enhance the stability and efficiency of RFT. Our comprehensive study demonstrates the superiority of RFT as a robust paradigm for continual post-training.