Different branch/MOS/unit. The third pic looks like MP's or something, the upper pics show UNSC Marines in standard body armor.
Also bear in mind, with sustained space travel, time dilation is a factor. Uniform and equipment standards change.
It's a bit of a plothole in how the chief wakes up in Halo 4 with the newest BR85 battle rifle,(With the blocky eotech-like sight and pic rails everywhere) sticky launchers and MA5D assault rifle when the UNSC was using the older MA5C and BR55(Battle rifle with the ACOG-looking scope that appeared in Halo 2) iterations throughout Halo 3.
Not to mention Cortana somehow physically modifying his armor while he was in cryo... That's kinda fucky. "Firmware update" indeed.
ETA: Oh, almost forgot. The reasoning behind exposed hard plate armor is the fact that they're fighting aliens that use suspended plasma weaponry. Armor has to absorb and dissipate the immense heat from those weapons, and a cloth exterior would burn at those temperatures, so there's no point. That's the original idea behind the art design, though Bungie let the art department get away with pretty much whatever they wanted in the name of artistic license for the most part.
So... "Because it looks cool."