Read the StdDev value. If it is zero, the images are 100% identical. If not, they are different. If StdDev is below 1.0, the difference is insignificant. To see where the differences are, add a Threshold layer on top. Move the slider to the far left, then slowly nudge it to the right. White means difference, black means identical.
If the op needs 100% accuracy, i.e. to know if two images are absolutely identical byte per byte, Photoshop rounds to 15-bit any loaded image so it won't be able to distinguish many 1-bit differences.
I would just load them in any language and compare them. In R this is so straightforward as:
img1=readTIFF("img1.tif", native=FALSE, convert=FALSE)
img2=readTIFF("img1.tif", native=FALSE, convert=FALSE)
ifelse(max(abs(img1-img2))==0, "Images are identical", "Different images")
Regards