TiG and MIG are both fine. The only difference is that it is easier to control the heat input with TIG for Chromoly. The material is more temperature sensitive to overheating. A competent welder can do both types of welding just fine. A bit of pre-heat for Chromoly is suggested but usually not needed for thinner material. It is also easier to mix your rod with the base material when Tig welding as opposed to MIG.
There are different types of Chromoly just as regular mild steel. Dependent upon the material and thickness dependent upon the welding process. Mild steel is more forgiving to weld and will bend more before failing. Chromoly usually fails in the heat affected zone because of overheating, no preheat prior to welding and cooling to quickly.