The S3 will have ridiculously better hardware and stock proprietary software, but official updates from Samsung will probably come no faster than they ever have, which is just not fast at all. To run the latest Android versions in the future, you will probably have to depend on independent developers releasing custom ROMs. The S3 would be great for someone planning to upgrade/replace within 6 to 12 months, or someone who is comfortable with rooting it and keeping it updated with dev releases.
The Nexus will not have Samsung branding or proprietary software (like Touchwiz) but will always run the latest open source Android OS that Google puts out, even a couple years down the road. Its hardware capabilities, though impressive in the current market, will soon be dwarfed by the likes of the S3 and other competitive models. If you can remain impressed by the Nexus's constantly current software and support and the decent hardware that it contains, then it will provide competent service with excellent longevity.
The Nexus is yesteryear's model, though. Verizon has had their Nexus for quite some time and Sprint seems to have gotten it the way younger siblings get hand-me-downs. That's less-than-stellar on Sprint's part, IMHO. It is a very solid phone with its own unique benefits, but personally, I am holding out for the quad-core supa-fast technologically sexy S3, and I will have faith in the dev community to keep it awesome for some time.