As far as character development and feels for character's well being, Shepard.
Hand to hand combat, MC wins if Shep is pure soldier. If Shep's a Vanguard, or anything else really, he wins in a landslide because of his powers.
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what if we gave MC the ability to fly
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Chief cant fly. But if he could: Shepard as Adept: Singularity and Warp for a biotic explosion. Engineer: Overload to take out shields, Incinerate to take out. Sentinel: Throw and Warp for a biotic explosions Infiltrator: Invisibility. Also Cryo Blast. Vanguard: Biotic Charge and Nova. Do it right and you can one hit Phantoms, Atlas' don't take long either. Chief wouldn't be too difficult. Also Shockwave-Charge is a biotic explosion. I think. Soldier: Shep is done for. No chance.