I would choose the S3. The N4 features low memory, no battery swap, no sd card, and all the multiple issues it has.
Samsung galaxy s3, the world's best selling phone, features a lot new features and have powerful specs.
Anyway, it depends on you.
-16GB memory is adequate for me & my uses
-I use to carry a spare battery for my GNex but I get a day from my N4 so no need
-N4 has more powerful specs
-N4 gets updates much quicker
-S3 has an older version of Android
-S3 has build quality problems as well
-S3 is about 5 months older than the N4
-S3's features like Smart Stay & pop-up browser / video are achievable on the N4 through Apps
-S3 from a carrier has bloatware
I have an S3 & an N4.
Both are great phones & it's difficult to determine which is better overall than the other.
Really, it boils down to what:
-network you're on
-price you want to pay
-you plan to do with your phone
-time frame you plan to keep it for
That said, my daily driver is the N4.