Using the QCD dipole picture of the hard BFKL pomeron, we derive the general expressions of the elastic and inelastic components of the proton diffractive structure functions. We obtain a good seven-parameter fit (including a secondary reggeon contribution) to data taken at HERA by the H1 and ZEUS Collaborations. The main characteristic features of the model in reproducing the data are discussed, namely the effective pomeron intercept, the scaling violations and the β-dependence. A difference obtained in the separate H1 and ZEUS fits leads us to analyze directly the differences between both measurements. Predictions on R, the ratio of longitudinal to transverse photon cross sections are performed and lead to very large values at high beta and large virtuality Q which may lead to a discrimination between models.