Predicting the mechanical properties of polysulfone (PSF) membranes from structural descriptors remains challenging due to extreme data scarcity typical of experimental studies. To investigate this issue, this study benchmarked knowledge-driven inference using four large language models (LLMs) (DeepSeek-V3, DeepSeek-R1, ChatGPT-4o, and GPT-5) against partial least squares (PLS) regression for predicting Young's modulus (E), tensile strength (TS), and elongation at break (EL) based on pore diameter (PD), contact angle (CA), thickness (T), and porosity (P) measurements. These knowledge-driven approaches demonstrated property-specific advantages over the chemometric baseline. For EL, LLMs achieved statistically significant improvements, with DeepSeek-R1 and GPT-5 delivering 40.5% and 40.3% of Root Mean Square Error reductions, respectively, reducing mean absolute errors from $11.63\pm5.34$% to $5.18\pm0.17$%. Run-to-run variability was markedly compressed for LLMs ($\leq$3%) compared to PLS (up to 47%). E and TS predictions showed statistical parity between approaches ($q\geq0.05$), indicating sufficient performance of linear methods for properties with strong structure-property correlations. Error topology analysis revealed systematic regression-to-the-mean behavior dominated by data-regime effects rather than model-family limitations. These findings establish that LLMs excel for non-linear, constraint-sensitive properties under bootstrap instability, while PLS remains competitive for linear relationships requiring interpretable latent-variable decompositions. The demonstrated complementarity suggests hybrid architectures leveraging LLM-encoded knowledge within interpretable frameworks may optimise small-data materials discovery.