TEM analyzes the crystal structure and nanoscopic details of cobalt carbide particles and is very effective for observing the atomic structure with high resolution. XPS is also useful for examining the surface oxidation of cobalt carbide or the bonding between cobalt and carbon atoms. XRD is widely used to determine the crystal structure and phase composition of cobalt carbide. This technique determines which phases the material is in by examining the arrangement of atoms that make up the crystal structure.
As Özgün describes the three methods mentioned are sensitive to different things. To characterize cobalt carbide, you could measure tensile strength or hardness or a lot of other things. The methods you use for characterization depend on what properties are important to you.
What is the best method? It depends (on what is important to you).