This paper deals with the study of calcium sulfoaluminate (CSA) and geopolymeric (GEO) binders as alternatives to ordinary Portland cement (OPC) for the production of more environmentally-friendly construction materials. For this reason, three types of mortar with the same mechanical strength class (R3 ≥ 25 MPa, according to EN 1504-3) were tested and compared; they were based on CSA cement, an alkaline activated coal fly ash, and OPC. Firstly, binder pastes were prepared and their hydration was studied by means of X-ray diffraction (XRD) and differential thermal-thermogravimetric (DT-TG) analyses. Afterwards, mortars were compared in terms of workability, dynamic modulus of elasticity, adhesion to red clay bricks, free and restrained drying shrinkage, water vapor permeability, capillary water absorption, and resistance to sulfate attack. DT-TG and XRD analyses evidenced the main reactive phases of the investigated binders involved in the hydration reactions. Moreover, the sulfoaluminate mortar showed the smallest free shrinkage and the highest restrained shrinkage, mainly due to its high dynamic modulus of elasticity. The pore size distribution of geopolymeric mortar was responsible for the lowest capillary water absorption at short times and for the highest permeability to water vapor and the greatest resistance to sulfate attack.