We compare two approaches to the description of pion Compton scatterin
g at moderate momentum transfer, one being based on local duality QCD
sum rules for the invariant amplitudes of the process, which have been
derived recently, and the other on the modified factorization formula
with Sudakov effects included. We find that perturbative QCD predicti
ons are dominant over those from QCD sum rules only for the scattering
angle greater than 40-degrees.