Accurate recognition of dysarthric and elderly speech remains challenging to date. While privacy concerns have driven a shift from centralized approaches to federated learning (FL) to ensure data confidentiality, this further exacerbates the challenges of data scarcity, imbalanced data distribution and speaker heterogeneity. To this end, this paper conducts a systematic investigation of regularized FL techniques for privacy-preserving dysarthric and elderly speech recognition, addressing different levels of the FL process by 1) parameter-based, 2) embedding-based and 3) novel loss-based regularization. Experiments on the benchmark UASpeech dysarthric and DementiaBank Pitt elderly speech corpora suggest that regularized FL systems consistently outperform the baseline FedAvg system by statistically significant WER reductions of up to 0.55\% absolute (2.13\% relative). Further increasing communication frequency to one exchange per batch approaches centralized training performance.