The international variant of the GSIII has a quad-core Exynos chip made in-house at Samsung. But in America, we're treated differently. Namely, U.S. variants see an LTE radio added and the Exynos taken away, replaced by a dual-core Qualcomm Snapdragon S4 clocked at 1.5GHz. Two GB of RAM support the phone, and 16 GB of internal storage will hold more than a few tunes, photos and videos. There's also a slot for microSD storage expansion.
The iPhone 5 packs the same internals (besides antenna frequencies) regardless of the country of destination. The processor is Apple's A6 dual-core SoC clocked at 1.3GHz. While that's slower than the GSIII, it's important to remember that Apple hardware and software are developed together, so Apple's hardware is usually much more efficient than the competition. Graphics are handled by a tri-core PowerVR SGX543MP4 (catchy, huh?). One GB of RAM rounds out the iPhone 5's kit. The iPhone 5 comes in fixed-storage variants of 16 GB, 32 GB and 64 GB, with each storage tier adding $100 to the phone's price.