Recycling concrete construction waste is a promising way towards sustainable construction. Indeed, replacing natural aggregates with recycled aggregates obtained from concrete waste lowers the environmental impact of concrete constructions and improves natural resource conservation. This paper reports on an experimental study on mechanical and durability properties of concretes casted with recycled aggregates obtained from two different parent concretes, belonging to two structural elements of the old Cagliari stadium. The effects of parent concretes on coarse recycled aggregates and on new structural concretes produced with different replacement percentages of these recycled aggregates are investigated. Mechanical properties (compressive strength, modulus of elasticity, and splitting tensile strength) and durability properties (water absorption, freeze thaw, and chloride penetration resistance) are experimentally evaluated and analyzed as fundamental features to assess structural concrete behavior. The results show that the mechanical performance of recycled concrete is not related to the parent concrete characteristics. Furthermore, the resistance to pressured water penetration is not reduced by the presence of recycled aggregates, and instead, it happens for the chloride penetration resistance. The resistance to frost–thawing seems not related to the recycled aggregates replacement percentage, while an influence of the parent concrete has been assessed.