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It's been fairly well established that the advantage that SW and ST have against 40k is mobility. The Imperium's biggest weakness compared to them is their relative slow and unreliable means of moving from battle to battle.
However.
Supposing the Imperium put the Federation in a position where it had to fight instead of doing Eldar-esque hit and run shenanigans, the Imperium would mop the floor with even the NG and later Enterprises. Is it because 40k tech is generally >9000 levels of bullshit power? Yup. But you asked, so there's the answer.
Also, I could imagine a Khorne Berzerker seeing a Klingon and his stop-motion grade fighting and just facepalming until it went through his ceramite plate. Honestly, I think the Klingon's would win just by insulting the CSM's knowledge of combat tactics to the point of suicide.
