An alcove has no single width. At floor level the skirting takes 1 to 2 cm off each side, the two side walls of the recess are rarely parallel, and the same recess measured at the top and at the floor gives two different numbers. Sofas have no single width either: the figure in a listing is often the seat width, and the arms add 15 to 25 cm on top of it.
So the two numbers that usually get compared are the widest reading of the recess and the narrowest reading of the sofa. Both are correct, and neither of them decides anything.
What has to be true
Sofa width across the arms, plus 2 to 3 cm on each side, has to be smaller than the narrowest point of the alcove. The margin covers the error in the measuring: walls drift, readings get rounded, and the hands lowering the sofa into the recess need somewhere to be.