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The influence of all transition element dopants on grain boundary (GB) cohesion in both W and Mo is investigated by means of high throughput density functional theory (DFT) calculations. We present site specific segregation energies to GBs and free surfaces (FS) of W and Mo and evaluate the strength of embrittlement of the individual solutes. The segregation properties for a consistent set of solutes allow an unprecedented comparison to previous DFT data and phenomenological models for segregation. Our DFT data show that the trends are very similar in W and Mo for the different solutes, while the comparison with available phenomenological models highlights the limits of band-filling and elastic models for GB segregation and strengthening.