Good question. If it was one squad of commandos vs. a single Spartan, the commandos would win, no doubt. However, in one on one, I'm not sure. They both have personal sheilds. I'd guess that the Spartan had better armor, and is probably stronger due to its augmentations. Where the spartans fail is their lack of weapons. They can carry two weapons and two types of gernades, whereas the commandos can cary a pistol, their DC-17/m with blaster, sniper, and anti-armor attachments, and an additonal gun, as well as five kinds of gernades.
The spartan's gernades don't really have much use except for blowing stuff up. I think that if the commando threw a EC gernade, the EC could take out the sheild, as well as the Spartan's computers in its suit, making him much weaker, as the suit gives a Spartan much of his strengh. Also, the commandos have the advantage of bacta, which seems to be more effective than just a med pack.
In my opinion, the commando would win because of more diverse and useful weapons.