Neither.
Wait until you're off contract, buy a Nexus 4, and get a SIM card from an AT&T MVNO (like AirVoice) or T-Mobile MVNO (like Straight Talk). There's no contract, little or no setup cost, and if the provider ticks you off, you can take your phone and walk.
Yes, there's the up front cost of the phone, but the Nexus 4 is (if memory serves) superior to the Galaxy S3 in terms of both hardware (fact) and software (opinion; I strongly prefer stock Android to Samsung's TouchWiz UI). Also keep in mind that the big 4 (Verizon, AT&T, T-Mobile, and Sprint) claim that they're selling you a "$600" phone (which is an artificially inflated MSRP) for $100 or less with a 2-year contract, but, believe me, you ARE paying for that phone through inflated monthly rates (rates, it bears mentioning, that DO NOT increase after your contract period is up).
I have a Galaxy Nexus with an AT&T SIM on Straight Talk (unfortunately, ST no longer offers AT&T SIM cards, but there are alternatives such as AirVoice if T-Mobile's network isn't competitive in your area) and I pay ~$49 a month for unlimited talk, text, and "web" (which effectively means if you're not silly about how much data you use, ST won't bother you).
Together, my wife and I pay less than $100 a month for our cell phone plans. The equivalent service would cost closer to $180 a month at Verizon (which, I'll admit, has a better network, but the difference is not worth anywhere near $80 a month).
TL;DR: Nexus device (currently the Nexus 4; the price point on the Galaxy S4 Google Edition is inane) + AT&T MVNO or T-Mobile MVNO SIM card = significantly cheaper than postpaid (contract) plans available through the big 4 cellular providers in the US.
Down with contracts! Up with consumer advocacy!