Argentina is clearly the larger of the two: about 2,782,703 km² km² against 7,706,009 km² km², roughly 2.8× at true size. Drag one onto the other on the map above to feel the gap.
Argentina sits in South America, Australia in Oceania. On the old Mercator map the latitude gap distorted how large each felt beside the other; at true size the answer is simply 2.8×.
The old Mercator map treated both about equally (1.5× vs 1.2× inflation), so at least their relative sizes were preserved — even if both were drawn at the wrong absolute scale.
Argentina fits 2× into Australia.