Obviously on a general basis, hardfacing is a more costly process and can supply a face with much more resistant materials than a case hardening process. The processes and end properties are in general far from equal.

Wikipedia:
Case-hardening or surface hardening is the process of hardening the surface of a metal object while allowing the metal deeper underneath to remain soft, thus forming a thin layer of harder metal (called the "case") at the surface. For iron or steel with low carbon content, which has poor to no hardenability of its own, the case-hardening process involves infusing additional carbon or nitrogen into the surface layer.

Hardfacing is a metalworking process where harder or tougher material is applied to a base metal. It is welded to the base material, and generally takes the form of specialized electrodes for arc welding or filler rod for oxyacetylene and TIG welding. Powder metal alloys are used in (PTA) also called Powder plasma welding system and Thermal spray processes like HVOF, Plasma spray, Spray and Fuse, etc.