Prompt Engineering Versus Model Selection for Cognitive Accessibility in Large Language Models: An Empirical Study

The promise of large language models (LLMs) for individuals with learning disabilities and cognitive impairments is significant, yet their practical accessibility remains limited by readability barriers. In improving output accessibility, both model selection and prompt engineering offer potential levers, but their relative importance remains unquantified. This study conducted a systematic investigation of prompt engineering versus model selection for enhancing cognitive accessibility of responses in four leading LLMs (Llama-3.3-70B, Llama-3.1-8B, GPT-4o, Claude-Sonnet-4.5). Three prompt engineering approaches were tested: Baseline (task only), Structured (organizational guidance), and Cognitive-Explicit (accessibility constraints grounded in working memory theory), across two task types (procedural and conceptual), resulting in a 3×2×4 factorial experiment (N= 240 responses), with readability quantified as Flesch Reading Ease scores. Prompt engineering accounted for 71.9% of variance (ηp² = 0.719,ppd= 2.49), reducing sentence length by 47% with minimal trade-off in lexical diversity. Task type also influenced accessibility, with procedural tasks yielding significantly higher readability than conceptual explanations (p< 0.001, ηp² = 0.231). Models exhibited differential responsiveness, reflected in a marginally significant Model × Prompt interaction (p = 0.068, ηp² = 0.052). Claude-Sonnet-4.5 achieved the largest gain (+43.41 points, +128%) and Llama-3.1-8B the smallest (+31.36 points, +64%). These findings establish prompt engineering as the dominant factor for cognitive accessibility in LLMs and offer actionable guidance for practitioners prioritizing accessibility in AI deployments for cognitive disability populations.