High energy QCD and hard diffraction at HERA versus Tevatron

We present and discuss two different topics where Tevatron and HERA data can be compared directly. A method allowing for a direct comparison of data with theoretical predictions is proposed for forward jet production at HERA. An application to the determination of the effective Pomeron intercept in the BFKL-LO parametrization from $d\sigma/dx$ data at HERA leads to a good fit with a significantly high effective intercept, $\alpha_P= 1.43 \pm 0.025 (stat.) \pm 0.025 (syst.)$. It is less than the value of the pomeron intercept using dijets with large rapidity intervals obtained at Tevatron. In a second part of this report, we make comparison between diffractive results at HERA and at Tevatron. We first give the parton distributions in the pomeron extracted from HERA data, and compare with hard single diffraction at Tevatron and diffractive dijets with a leading antiproton data.