Accurate predictions of cloud condensation nuclei (CCN) activation are essential for reducing uncertainties in aerosol-cloud interactions and climate projections. Most large-scale aerosol models represent particles as compositionally averaged internal mixtures and assume constant surface tension of water, neglecting particle-level compositional variability and surfactant-driven reductions in surface tension. Here we use the particle-resolved model WRF-PartMC to quantify how these simplifications affect CCN predictions by comparing particle-resolved (PR) and composition-averaged (Comp) aerosol populations under constant surface tension (CST) and effect surface tension (EST) treatments. Within this framework, PR-EST case provides the most physically detailed reference, and Comp-CST case represents a modal-like aerosol representation in large-scale models. We find this modal-like representation underpredicts CCN by ~19% on average relative to PR-EST reference. This bias reflects two opposing effects: neglecting surfactants suppresses activation, whereas composition averaging shifts activation in both directions depending on particle size and composition. A particle-level decomposition shows that Comp-EST modifies activation through coupled changes in hygroscopicity and surface tension that oppose each other, producing compensating shifts in particle critical supersaturation. These responses produce opposing biases across particle size ranges, with enhanced activation in Aitken mode and suppressed activation in accumulation mode. When EST is included, the remaining bias from composition averaging is substantially reduced, with Comp-EST case differing from the PR-EST reference by ~6% in domain-mean. These results demonstrate simplified aerosol schemes can produce apparently reasonable CCN predictions through compensating errors, even when underlying activation physics is misrepresented. Incorporating effective surface tension therefore offers a practical pathway to reduce structural biases in large-scale models.