You can subtract them and look for 0's. For grayscale images:
matchingPixels = (double(image1) - double(image2)) == 0;
imshow(matchingPixels);
To find area of matching pixels, you can use sum(), bwarea() or regionprops():
area1 = sum(matchingPixels);
area2 = bwarea(matchingPixels);
% To use regionprops to find areas of all matching regions.
labeledImage = bwlabel(binaryImage);
measurements = regionprops(labeledImage, 'Area');
area3 = sum([measurements.Area]);
For color images, you have to check each color channel for matches.
For binary images use the dice() function, introduced in R2017b:
Description
similarity = dice(BW1,BW2) computes the Sørensen-Dice similarity coefficient between binary images BW1 and BW2.
