[wycx]

In this context energy=wavelength=frequency, and hard x-rays means x-ray with energies > approx. 5 keV. I am assuming properties they are after in their particular context are <i>tunable</i> hard x-rays with with relatively narrow bandwidth, such that they can tune the energy/frequency/wavelength of their beam to be above the absorption edge of particular elements in the pigments in paintings and compare the x-ray fluorescence maps above and below the absorption so they can see where particular pigments are and thus paintings hidden below the visible painting.

One big advantage synchrotrons have is flux over a broad spectrum. When you want monochromatic x-rays you can start with broad spectrum x-rays from a synchrotron source and throw almost all of the photons away, and still have orders of magnitude more x-rays in your 1 eV bandpass beam than the flux of a laboratory source, (even if it has a peak in its spectrum at the energy you want). The plots on slides 4-6 linked in the first comment [1] demonstrate this clearly.

However, the energy range where inverse compton scattering sources seem most attractive are at energies >100 keV where it appears there is the potential for inverse compton sources to approach and even outperform synchrotron bend-magnet sources (slides 31 to 35), particularly in comparison to bend-magnets/wigglers at synchrotrons with lower storage ring energy than facilities like ESRF (6 GeV). High flux at higher energies (>100 keV) is difficult to generate at the more common 2.0-3.0 GeV storage rings.

[1] https://indico.cern.ch/event/1088510/contributions/4577523/a...