Well, both sides are the result of genetic modification. Without bringing the possibility of the Astartes having super abillities or psionics (it all depends on the lineage of the paticular gene seed, they do vary in power) it comes largely down to weapons.
I think most people are wrong in assuming that a Halo assault rifle would be totally ineffective against Space Marine armor. Sluggas and Auto Pistols can bring Space Marines down just fine, especially if you shoot them enough times.
The big factor in deciding this fight is probably going to be a bit that I don't think anyone else mentioned, and that is quite simply that Master Chief has a personal force field. That whole "regenerating health" gimmick that gets such mixed reviews.
To be blunt, personal Force Fields do exist in Warhammer 40k, and they are a BIG deal, a major artifact from the dark age of technology. Something like that is a major force on the battiefield all on it's own, and space marines DO have trouble dealing with gimmicks like that.
Dealing with this conceptually, rather than getting into specific game mechannics on either side (especially seeing as I only really have RPG stats for Warhammer 40k, via things like Rogue Trader, Dark Heresy, and Deathwatch), I think your typical Astartes would have some serious difficulty doing damage to the guy, especially seeing as his force field would keep regenerating by it's very nature.
In general I'd say MASTER CHIEF as a major hero, would trash your typical Astartes. You put him up against a hero level Space Marine armed with chapter relics, and it would be a lot more even. Unit for Unit I'd say the Spartans would bet a bit better, largely because of the shields, overall I'd say the two types of troops are almost identical, but the Astartes as they exist as of the time of Warhammer 40k are a mere shadow of what they once were, using a lot of technology they don't fully understand, and having lost a lot of their best tricks due to simple decay over thousands of years. The Spartans on the other hand are fully prepped with state of the art tech that has just come off of an assembly line (so to speak) as opposed to spending thousands of years being repaired and rebuilt.
To get into things mechanics wise, if someone was to ask me to build Master Chief or a Spartan within say the "Deathwatch" mechanics (ignoring the basic character generation, just assiging relevent stats) it would be very similar to what the Space Marines have, but as I said I'd be loading him with Archaotech for things like the force field, and he'd wind up being a borderline munchkin.
I'd also remind people that Space Marines are tough, but they get trashed by relatively ordinary stuff all the time. Within the Warhammer 40k universe, I don't even think they are pound for pound the best unit the Imperium can actually field. A lot of the special forces units of groups like The Imperial Guard can come very close, and you have guys like Spyrers, who are hive nobles with powered armor, who have weapons and gimmicks at least as good as the Space Marines overall when you look at what they are actually packing. It's also not totally unheard of for relatively normal guys, albiet ones who are heroic, like various Comissars and such to be able to best enemies like Chaos Marines in hand to hand combat.
I think the problem is that it depends on who is writing things, and how "yahoo" they tend to be getting at the moment. Conceptually, the Astartes are tough, but far from being invincible. Even in the minatures game, a couple of bad (for the marines) rolls and a squad with autoguns or sluggas can gun down a squad of elite space marines.