The dynamic modulus of asphalt mixtures (|E*|) is a key mechanical parameter in the design of road pavements, yet direct laboratory testing is time- and resource-intensive. This study evaluates two predictive models for estimating |E*| using data from 62 asphalt mixtures containing reclaimed asphalt: a grey relational analysis–multiple linear regression (GRA-MLR) hybrid model and a mechanistic sigmoidal model. The results showed that the GRA-MLR model effectively identifies influential variables but achieved moderate predictive accuracy (R2 values varying from 0.4743 to 0.6547). In contrast, the sigmoidal model outperformed across all temperature conditions (R2 > 0.96) and produced predictions deviating by less than ±20% from measured values. Temperature-dependent shifts in factor influence were observed, with stiffness and gradation dominating at low temperatures and reclaimed asphalt (RA) content becoming more significant at higher temperatures. While the GRA-MLR model is advantageous, offering rapid assessments and early-stage evaluations, the sigmoidal model offers the precision suited for detailed design. Integrating both models can balance computational efficiency and provide a balanced strategy, with strong predictive reliability to advance mechanistic–empirical pavement design.