The global rise in temperature and the desert climatic conditions prevalent in Middle Eastern countries have exacerbated rutting distress in heavily trafficked highways. Conventional asphalt binders with a high-temperature performance grade (PG 70) have proven inadequate under such extreme conditions, necessitating the development of modified binders with enhanced high-temperature performance. While polymer modification using styrene-butadiene-styrene (SBS), an elastomeric polymer, and ethylene-vinyl acetate (EVA), a plastomeric polymer, has been widely studied, limited research provides a direct comparison of their effectiveness at both the binder and mixture levels under extremely high-temperature conditions. This study addresses this gap by evaluating SBS and EVA at 2%, 4%, and 6% by weight of asphalt cement, with a focus on their rheological, chemical, and mechanical properties. At the binder level, properties examined included the physical properties: penetration, softening point, viscosity, mass loss due to aging, storage stability, and specific gravity. The Dynamic Shear Rheometer (DSR) was used to assess the high-temperature performance grade (PG) and conduct Multiple Stress Creep Recovery (MSCR) tests. The results revealed that SBS significantly enhanced high-temperature performance, with 4% SBS and 6% SBS achieving PG 100, compared to PG 70 for both the unmodified and EVA-modified binders. At the most critical testing temperature of 76 °C and the highest stress level of 3.2 kPa, SBS-modified binders exhibited the lowest non-recoverable creep compliance (Jnr) and the highest elastic recovery (R), significantly outperforming EVA-modified binders and the reference binder (RB). At the mixture level, dynamic creep testing confirmed the ranking of asphalt mixes in terms of resistance to permanent deformation, with the following order: 4% SBS > 6% SBS > 6% EVA > 4% EVA > 2% SBS > 2% EVA > unmodified mix. These results, further supported by ANOVA analysis, indicate that SBS-modified mixtures exhibited superior rutting resistance compared to EVA-modified and unmodified mixes. This study provides quantitative insights into the comparative performance of SBS and EVA in extreme hot climatic tempertures, reinforcing the superior effectiveness of SBS in enhancing high-temperature properties. Consequently, SBS emerges as the more suitable modifier for regions experiencing extreme hot climatic conditions. Field validation is recommended to confirm these laboratory findings in real-world applications.