Nearly a tie: Iran and Mongolia differ by barely -4%% in area — about 1,622,847 km² km² against 1,560,428 km² km².
Both sit in Asia, 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 1× you see above.
The old map muddied it further: Mercator inflates Iran about 1.4× and Mongolia about 2.2×, so on a Mercator-style map this pair appears 1.5× apart instead of the true 1×.
Iran fits 0× into Mongolia.