The GSIII's 8MP shooter is packed to the gills with features. Samsung adjusted the software to eliminate shutter lag and brought great features like burst mode (which takes a rapid set of photos) to the fore. It records video in 1,080p. The thing is, the iPhone 5's camera packs nearly all of these features too (it lacks burst mode in its standard software.) Both phones also pack in 1,080p video recording.
While there is basic feature parity between the two cameras, most outlets give a slight edge to the iPhone 5's camera for better low-light performance and better panoramic photo stitching. But, there is a bright spot for Samsung here; the GSIII's front-facing camera checks in at 1.9MP compared with the iPhone 5's 1.2MP sensor.