I keep getting this question so i turned to Comic Vine
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You should give some parameters.
First and foremost, Commander Shepard is not a defined character, just to begin with it has six different classes and they are very different between themselves.
But let's try, in a H2H without any firearms but with all rest, I'd say: Adept and Vanguard > Chief > Other 4 classes. As skilled as Shepard may be, I don't think he will be able to handle the Spartan. His stronger and his armor will make a huge difference and should offer great resistence against tech powers. However, not so much agaisnt biotics. Shepard is extremely skilled and will be able to use its powers to deadly efficiency.
In a standard random encounter is harder to say. I guess with weapons Master Chief will be able to even the odds against a biotic Shepard... Chief superior armor might win the day. Skil wise I don't see much difference, not in the battlefield anyway. It will be close, but Chief can endure more.
With some prep time I go with Shepard. He is a superb commander and has access to enough firepower to counter Chief outstanding armor.