Nearly a tie: Libya and Sudan differ by barely -13%% in area — about 1,626,369 km² km² against 1,863,027 km² km².
Both sit in Africa, 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 0.9× you see above.
The old Mercator map treated both about equally (1.3× vs 1.1× inflation), so at least their relative sizes were preserved — even if both were drawn at the wrong absolute scale.
Sudan fits 0× into Libya.