They use different algorithms. regionprops gives the number of pixels while bwarea gives some kind of weighted area that depends on the shape of the boundary. This is described in the documentation for bwarea
The white to black ratio is
totalPixels = numel(binaryImages);
numWhitePixels = sum(binaryImage(:));
numBlackPixels = totalPixels - numWhitePixels;
ratio = numWhitePixels / numBlackPixels;
