Argentina is clearly the larger of the two: about 2,782,703 km² km² against 1,296,279 km² km², roughly 2.1× at true size. Drag one onto the other on the map above to feel the gap.
Both sit in South America, so this is a same-region comparison: the new Equal Earth map draws both with the same honest geometry, and the real gap is exactly the 2.1× you see above.
The old map muddied it further: Mercator inflates Argentina about 1.5× and Peru about 1×, so on a Mercator-style map this pair appears 3.1× apart instead of the true 2.1×.
Peru fits 2× into Argentina.