  We present recent experimental data from the H1 and ZEUS Collaborations at
HERA for diffractive dijet production in deep-inelastic scattering (DIS) and
photoproduction and compare them with next-to-leading order (NLO) QCD
predictions using diffractive parton densities. While good agreement is found
for DIS, the dijet photoproduction data are overestimated by the NLO theory,
showing that factorization breaking occurs at this order. While this is
expected theoretically for resolved photoproduction, the fact that the data are
better described by a global suppression of direct and resolved contribution by
about a factor of two comes as a surprise. We therefore discuss in some detail
the factorization scheme and scale dependence between direct and resolved
contributions and propose a new factorization scheme for diffractive dijet
photoproduction.
