Speed goes to John, as he dodged bullets and even plasma projectiles, and viewed the combat of trained infantrymen like ODSTs in slow motion.
Strength and AP goes to John, being capable of knocking out Spartans in as little as 3 blows, even though their armor can withstand futuristic tech-level firearms of both kinetic and directed energy, as well as absurdly high falls. Going by the profiles; MC can also lift better, being able to lift at least 5 tons, and the profile of Eternal Warrior is a bit vague on how heavy the Giant's head is. (A scan would be helpful). He can also strike better,
at least 167 MJ.
Durability goes to John. One has energy shielding, which can withstand
triple digit megajoule level energy blasts (and even the 1.5 GJ fuel rod cannon at close range). The other does not, and MC also has his dura feats mentioned previously, even without shielding.
Although the Warrior does have his perks. He has over 6 millennia of experience (Mastering 500 forms of combat and seemingly capable of using any melee and ranged weapon in the most efficient manner), fought armies and hordes of demons and zombies, even while his chest was pierced. But MC doesn't lag behind in wit, even against overwhelming odds (such as The Flood on High Charity), he still manages to come on top (and that luck of his).
Chief still holds a technological advantage, in weapons, armor, and training (and Cortana), as well as the reasons I gave before. Experience can only get you so far, after all. Voting John.
And yea, how does his Low Godly regen work? How long does it take?