In terms of weapons, let's just compare the human projectile weapons rather than Beam Rifles and whatnot. If we look at the rifles, the strongest non-sniper rifle in Crysis 2 is the Grendel, which shoots hollow-point bullets. It's been stated multiple times that only armor-piercing and high-explosive rounds do noticeable damage to shields. In the case of AP rounds, individual bullets do very little damage. Antipersonnel rounds are near-useless against shields, but let's just say that the Grendel's as powerful as an MA5B from Halo, which shoots AP rounds but suffers from a lack of spring strength. Anyone who's played Halo would know that the BR55 (which fires large-caliber rounds that don't even exist yet in rifles) and the DMR (which fires the same caliber of bullets as the MA5 assault rifles, but at a much higher velocity) would beat the Grendel at any range. And the SCAR won't do much damage due to its small bullets--it would be no more damaging than an M7 SMG.
The Gauss Rifle would pose a threat to the Master Chief, but the Chief's sniper rifle fires an extremely massive round that's gas-powered and fin-stabilized for pinpoint accuracy. So they might be equal in power. The DSG-1, on the other hand, would not be able to take the Chief down quickly.
In close quarters, the Chief has his M90 shotgun, which is 8-gauge. 26th-century technology has made such large shells feasible. By contrast, Alcatraz doesn't have anything more powerful than the Marshall, which is only 12-gauge. It probably won't even beat the Brute Mauler head to head.
The only time Alcatraz can do much is when he has a JAW. Assuming it's as powerful as the Chief's M19 SSM Rocket Launcher (which it isn't), Master Chief still has a slight advantage due to his shields and armor, which are stronger than the Nanosuit's armor mode. However, we've seen the Chief's rocket launcher take down light aircraft in 1 shot. The JAW takes more than 1 to down a helicopter and lots more to destroy a Ceph gunship--which the Chief could probably take down within 2 hits.
For the reasons above, Spartans would beat Nanosuits in a fight. This isn't to say that Nanosuits svck though--its stealth and anti-cloak capabilities are better than the MJOLNIR's. However, this isn't enough to turn the tables, simply due to the fact that Nanosuits lose in nearly every other category. Like I said multiple times before, the only reason Spartans are able to beat the Nanosuits is because of the 500-year difference in technology.