Well i've thought about it for a while. I think that Spartans would be better fighters but the Space Marines would be better soldiers. The Spartans have better biological upgrades for quick battles but would falter when they need to fight for days on end.
Though their weapons would be subpar.
Ehn... I've honestly seen that gamed out a few times. Take the armor from both of 'em and a Space Marine would kick the crap out of a Spartan pretty much repeatedly. Give them the armor and... well, same thing. They operate pretty much in the exact same operational niche, only the Marines are considerably more biologically enhanced (in pretty much every way -- Marines are agile like you wouldn't believe, actually, and tend to have pretty impressive cognitive improvements, as well), honestly better trained, and overall have the better equipment. It's not really a matchup at all.
Spartans are a bit ahead of some of the better Imperial Guard critters (Well, possibly barring the assassins and similar specialists), from what I recall, but they're on average still considerably worse than most Marines. Master Chief or some of the more experienced Spartans might have a better chance of giving a good go of a Spartan vs Marine matchup, but pound for pound the Marine's the better warcritter.
Spartans would have a bit of an advantage on a C&C front if the AI piggybacked along, and possibly even without that, but they're definitely not the better fighter of the comparison... or soldier, really.