Let's assume an affine transformation between the moving image and the target image you want to register. If you know the ground truth (i.e. you know the scaling s, rotation t and translations T parameters between the two images, because you generated them artificially, for instance), a possibile solution is to evaluate the Root Mean Square Error between the estimated one s', r' , T' adn the real one s,r and T.
If you don't know the ground truth (this is common when we work with real data), the evaluation become more complex. I would suggest you two cases:
1) If the images are monomodal (same sensor, same intensity scale), you could evaulate the final results in terms of some similarity measures at pixel level (such as Mean Square Error or Normalized Mutual Information, or many others) between the portions of both images that overlap.
2) If the images are multimodal (different sensors), the previous analysis might be not suitable. As first attempt, you can try to merge the registered moving image and the target image (using different transparencies and false colors) and give a qualitative evaluation.
yes, it is extremely easy with MATLAB. However, since I suppose you need to save the deformed moving image to be used in your MATLAB script, I would suggest you to save it in an uncompressed format (or 100 QF JPEG), in order to avoid a small bias in MSE due to the compression.