Since I am far too lazy to actually think of how this would work out considering the situation both are in, I think of this fight as an open room with MC capping Doomguy before Doomguy can do anything.
Disintegrated? I hope that weapon can pack a decent punch. Master Chief doesn't exactly have a frail piece of metal for armor. The heat at entry through atmosphere and the impact on Earth after entry are both EXTREME showings of durability.
This might shock you, but a bullet has greater piercing force than a rocket. And a seek and destroy battle is in no way a disadvantage for Master Chief. His motion detector sense people at quite the mighty distance, not to mention his super hearing and reflexes.
As for tanking a rocket, that's not at all very impressive. Master Chief doesn't even get hit by them, so although he can tank them, he doesn't have to I can see Master Chief wait around the corner, and when Doomguy is near he comes around the corner and apply the precious 50 ton force on his skull.
He can take several from the Cyberdemon... To the face...
And bullets having higher penetrating power than a rocket? Unless your talking Sabot AP rounds, then don't get your hopes up on that thought...
As for disintegration... the BFG utterly SHITES on ANY Covy plasma weapon short of the Wraith Cannon or Scarab main cannon, NEITHER of which Cheif could take a direct hit from.
And if you beleive Cheif has strength or speed advantages, that can easily be rreversed with the use of the Hellstone, it's powers make Cheif utterly impotent because of invulnerability, heltime and strength enough to GREASE demons in one punch... and I mean grease literally, like half a square mile of fishpaste that was once solid living flesh of demons. MC has NOTHING on the hitting strength enough to cause that kind of damage, thats borderline Gouki level.
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If we take them at their best Doomguy wins with all the overpowered items he can get. MC dose not stand a chance against that it's not even debatable it's like putting a guy in a wheel chair up against Mike Tyson in his prime