The difficulty is that the two spectra have different energy resolutions, so one cannot subract the raw spectra from each other. It is necessary to do a conventional peak fitting first. In essence this creates a spectrum in analytical form that can be redisplayed with arbitrary resolution. Then the two spectra can be overlaid. The peak fitting must be done with great precision because the analysis usually results in finding a small difference between large numbers, and errors are magnified.
N provides and interesting example of both the difficulties and the power of the method.
The strong state at 3.5 MeV in 13 N is the only state near the ground state that can be used for matching the spectrum near but not including the Fermi peak. N taken with 120 MeV protons. It is apparent that the peak shape includes a non-gaussian tail. Less apparent is that the shape of the 3.5 MeV peak is not the same as that of the ground state peak. One can also compare the peak fitting with sums, since the peaks are well separated.