In this study, we developed a new type of composite with improved thermophysical and mechanical properties. This composite is made of aerated concrete based on two types of additives, and we aimed to choose the best one. The main raw materials for manufacturing cellular concrete are sand, lime, cement, water, and aluminium powder. We replaced natural sand with olive pomace sand and shell sand, using replacement percentages of 10%, 20%, 30%, and 40%. We conducted a comparative study of the results to ultimately choose the one that yielded the best results. The thermomechanical properties, durability, and physical properties of the composites were studied. We finally concluded that both types of replacement reduce the mechanical properties of the material, but shell sand gives better results than olive pomace sand. We also found that composites based on olive pomace sand have a higher water absorption coefficient than those with shell sand, which weakens the material, probably due to the porous structure of olive waste and the lack of bonding between the matrix and grain. In terms of thermal properties, both sands exhibited increased thermal conductivity by 28.5% and 32.7% for a 10% replacement rate for olive pomace waste and shell waste, respectively, but this remains an acceptable value, as aerated concrete is already known for its thermal insulation properties.