Fillers have been widely used in natural rubber (NR) products. They are introduced to serve as a strategy for modifying the final properties of NR vulcanizates. Silica and calcium carbonate (CaCO3) are among the fillers of choice when the color of the products is concerned. In this case, a special focus was to compare the vulcanizing efficiency of NR filled with two different filler types, namely nano-sized silica and micrometer-sized CaCO3. This study focused on the effects of the loading level (10–50 parts per hundred parts of rubber, phr) on the final properties and structural changes of NR composites. The results indicated that increased filler loading led to higher curing torques and stiffness of the rubber composites irrespective of the type of filler used. The better filler dispersion was achieved in composites filled with CaCO3 which is responsible for less polarity of CaCO3 compared to silica. Good filler distribution enhanced filler–matrix interactions, improving swelling resistance and total crosslink density, and delaying stress relaxation. The modulus and tensile strength of both composites also improved over the content of fillers. The CaCO3-filled composites reached their maximum tensile strength at 40 phr, exceeding, by roughly 88%, the strength of an unfilled sample. Conversely, the maximum tensile strength of silica-filled NR was at 20 phr and was only slightly higher than that of its unfilled counterpart. This discrepancy was ascribed to the stronger rubber–filler interactions in cases with CaCO3 filler. Effective rubber–filler interactions improved strain-induced crystallization, increasing crystallinity during stretching and reducing the strain at which crystallization begins. In contrast, large silica aggregates with poor dispersion reduced the overall crosslink density, and degraded the thermomechanical properties, tensile properties, and strain-induced crystallization ability of the NR. The results clearly indicate that CaCO3 should be favored over silica as a filler in the production of some rubber products where high performance was not the main characteristic.