I think John has got this one in the bag...
Speed wise, John >>> Zero. SPARTAN II's are genetically superior specimens even before the SPARTAN II Program. Dr. Halsey screened each SPARTAN II candidate based on certain genetic markers indicating physical and mental superiority. At 14 years old (the time where John and the rest of the SPARTAN II's were subjected to the augmentation procedures), Dr. Halsey remarked that John, at 14 years old, "had the body of an 18 year old Olympic Athlete, and a mind the equal of any Naval Academy's Honors Graduate". I'd say that puts John in the top 1% of the human population pretty easily.
Then, John was subjected to the SPARTAN II Augmentations. This included several surgical and hormonal alterations of his body. These augmentations included...
Cermanic Carbide Ossification- Advanced material grafting onto his skeletal structure to make bones virtually unbreakable.
Muscular Enhancement Injections- Protein complex is injected intramuscularly to increase muscle density and decrease lactase recovery time. John, after rehabbing from his augmentations, was able to single arm curl 40 kilos (approximately 88 pounds), at the age of 14, before the augmentations to his physique really had time to pay dividends. During the same gym session, John fights, and accidentally kills 4 ODST Hell-Jumper Commandos in hand to hand combat.
He likely got far, far stronger as time went on, as we have incidents of him breaking Sanghelli necks with punches later (Elites are physically on equal footing with SPARTAN II's).
Catalytic Thyroid Implant- A platinum pellet containing HGH is implanted into the thyroid to further boost growth of skeletal and muscle tissues. This augmentation likely worked in sync with the muscular injections, and turned John into a titan of a man, standing well over 2 meters in height and weighing approximately 290 pounds.
Occipital Capillary Reversal- This augmentation provided John with a marked visual perception increase, and allows him to virtually see in the dark, even without his gear.
Superconducting Fibrication of Neural Dendrites- This is probably the game changing augmentation. This augmentation boosted John's reaction time to about 20 milliseconds, although Chief Mendez stated they are impossible to chart with any accuracy, and believes the SPARTAN II's reaction times are significantly faster in combat situations. We have evidence of that increased reaction time by John dodging a stun round fired by a trainer at point blank range during a training exercise.
This isn't counting the MJOLNIR MK. VI armor that John wears. The armor, coupled with Cortana's onboard interfacing with the armor and John, further increases John's strength, speed, reflexes, and durability. The Mark IV armor doubled John's strength, which was already pretty impressive, considering that all of the SPARTAN II's could lift double their weight (I'm assuming over their heads), which was double the norm due to the enhancements of their physiques. I can only assume that as the newer versions of MJOLNIR became available, the amplification of his abilities increased as well.
John takes this due to the massive physical disparities between him and Zero, and John's own remarkable skill in hand to hand and ranged combat.