Side-by-side is the hardest: trying to retain one image in memory and then mentally overlaying it onto the other image requires nontrivial effort. In Rensink's Change Detection (2002), Rensink notes that "trying to 'spot the difference between two side-by-side images will be a rather different activity than trying to detect the change in a pair of sequentially presented images'."

As for detecting differences in the presence of flicker, R.A. Resnik's flicker paradigm (see also here) notes that the display of the blank field "swamps the local motion signals caused by a change, short-circuiting the automatic system that normally draws attention to its location. Without automatic control, attention is controlled entirely by slower, higher-level mechanisms which search the scene, object by object, until attention lands upon the object that is changing. The change blindness induced under these conditions is a form of invisibility: it can become very difficult to see a change that is obvious once attended."

The third method here is having the images dissolve into each other (in this case by varying the opacity of the overlaying image). I find that this method makes the difference obvious, and it takes little cognitive effort to detect it: I can be focusing almost anywhere on the photo and my eye will notice the change. There is also a strange sense of relief, a small endorphin/dopamine rush, when the difference is revealed this way.