Kazakhstan is clearly the larger of the two: about 2,712,747 km² km² against 1,560,428 km² km², roughly 1.7× at true size. Drag one onto the other on the map above to feel the gap.
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 1.7× you see above.
The old Mercator map treated both about equally (2.3× vs 2.2× inflation), so at least their relative sizes were preserved — even if both were drawn at the wrong absolute scale.
Mongolia fits 1× into Kazakhstan.