Be wary of non-OEM batteries, just be judicious in researching whatever you buy has a solid, reliable history. If possible, just pick up an OEM battery along with an external battery pack.
(Also keep in mind that with the S3 the NFS chip is in the battery, not the phone body itself so if you rely on any NFS functionality be sure to get an Samsung OEM, or a third-party battery that specifically states it's included.)