Patient-reported data has become increasingly important in chronic disease management to enable continuous monitoring of the progression. However, it remains unclear how to design patient-centred digital health solutions that promote engagement, increase self-disclosure, and thus contribute to accurate assessments. Optimising the design of such systems is particularly crucial for users with cognitive impairments and fatigue, as these factors can increase the burden on respondents. In a cross-sectional survey study within multiple sclerosis care (n = 162), the effects of an embodied conversational agent (ECA) are evaluated compared to an audio-based agent and a media-enriched form. The results showcase a moderating role of the patients' disabilities and indicate that an audio-based agent effectively balances the needs of a broad patient population while optimising data quality. Nonetheless, the ECA was associated with the highest honesty-accuracy of disclosure and the lowest effort. Supplementary analyses reveal that willingness to disclose sensitive information and preference for ECAs depend on users' general perception of technology as stressors, influenced by the severity of their symptoms. This paper contributes to the human-computer interaction literature by informing the design of patient-centred solutions such as digital therapeutics and offers practical implications for their personalisation.