DAC stands for digital-to-analog-converter. This is the piece of hardware in your phone that converts the digital source of your music (mp3, for example) to an analog signal that your headphone recognizes and converts to sound. Amps and DACs are two different items but can be found bundled together in many devices.
If you root your phone, you could acquire another DAC, but to be clear: this is a piece of hardware. I do not think root is required to use another DAC. A list of compatible DACs for the S3 can be found here:
As reported by some users here, a stock iPhone 4 outcompetes a stock (USA?) S3:
Assuming you live in the US, you may have issues with carriers if you buy the international version of the S3 (I-9300). I am not totally sure on this. I know you can, however, convert a US version (CDMA network) to a GSM phone. As far as sound quality goes: Wolfson DACs receive a lot of praise around here, but I have yet to test the international (Wolfson DAC) against the US version.
You should have no trouble driving your Superlux HD661s with either version of the S3, assuming the given stats are correct for your cans:
Sensitivity102 dB SPL (1mW) at 1KHz
Rated Impedance 68 @ 1KH