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It can be seen that the highest energy point is significantly different in the two plots. On my plot the point is below the line indicating the exponentially-cutoff power-law (PLEXP) model, and has an E^2dN/dE flux of 1.5E-13 erg/cm^2/s (or 9.2E-8 MeV/cm^2/s). On Jean's plot the point lies above the PLEXP curve and has a flux of approximately 2.2E-6 MeV/cm^2/s, a factor of approximately 20 larger than on my plot.
In the gll_pscP72Y_v2r1 FITS file this spectral point has:
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This power law is depicted on my plot as a red power law covering the range 10-100 GeV (the PL fits from the other bands are also shown). Numerically integrating the red PL function also gives 1.25e-09. Calculating E^2dN/dE at the mid point gives 31.6^2*9.3e-14 = 9.3e-11 GeV/cm^2/s = 1.5 erg/cm^2/s, in agreement with the point depicted on the plot.
This discrepancy occurs between Jean's and my plots for all the PLEXP models, for points above the cutoff energy. Flux points for sources with power-law spectra look to agree. I have not studied the LOGP models in much detail.