Mexico is clearly the larger of the two: about 1,962,279 km² km² against 1,296,279 km² km², roughly 1.5× at true size. Drag one onto the other on the map above to feel the gap.
Mexico sits in North America, Peru in South America. On the old Mercator map the latitude gap distorted how large each felt beside the other; at true size the answer is simply 1.5×.
The old Mercator map treated both about equally (1.2× vs 1× inflation), so at least their relative sizes were preserved — even if both were drawn at the wrong absolute scale.
Peru fits 1× into Mexico.