In the last decades, there are many reports on the use of composites as reinforcement of structural elements under compression, especially regarding the confinement of concrete structures, but works on stone or masonry columns are limited. Initially, FRP jackets were used because their high structural performance. However, they present some drawbacks like aesthetics or water impermeability, which can affect their applicability in historical constructions made in stone. Recently, FRCM appeared as an alternative with better compatibility with masonry structures. In the present study, a comparison between different composite materials to confine masonry specimens was made. FRPs with carbon or glass fibers and epoxy matrix, and FRCM with basalt or glass fiber mesh in a cementitious matrix were used to confine masonry, made in calcarenite cylindrical pieces and lime mortar. Strength and ductility gains under compressive loads were measured, and compared to the recommendations of different guidelines. Unidirectional FRPs were the optimal solution from a strengthening point of view. On the other hand, FRCM confinement offered more ductility than unreinforced masonry, but showed a softening behavior. Finally, regarding the studied design codes, the specific parameters included for masonry structures seemed enough to obtain accurate predictions of the compressive strength increase due to the confinement with the tested composites.