what is basic difference between these two techniques with respect to the analysis of different metal oxides (like MoO3 and IrO2) in mixed oxide matrix..?
HAADF-STEM is an imaging mode in TEM. Elemental mapping (assuming you're still referring to TEM) can be done in EELS or EDX (or both at the same time), and can be done simultaneously to a HAADF-STEM imaging.
For example, in the last figure of the supplementary of our recent paper
We did elemental mapping by EDX simultaneously with HAADF-STEM image acquisition (and then averaged the data over the vertical direction to present line profiles).
HAADF-STEM is a Z-contrast high resolution electron microscopic imaging technique whereas Elemental Mapping (assuming EDX or EELS) is a spectroscopy technique. Hence, rather than considering these two techniques as a complementary to each other, information obtained from both technique can be combined to get better idea about the composition of the metal oxide.