Per industry standards, each class must meet the minimum read/write speeds:
Class 10 = 10 MB/s
Class 6 = 6 MB/s
All UHS-1 cards: 10 MB/s
I can't find any info that says the S3 is a UHS-1 compatible host, which means it would revert to the industry standard class ratings.
Theoretically the chances are greater that a class 6 card will be at higher risk of choppy HD recorded video.
That said, I doubt the video quality on this phone warrants a class 10, especially if Sandisks own benchmarks are what they say they are.
But an S3, or any other mobile phone, can't wirte to a SD card at class 10 speends. So the only time it would come into play is when it is reading from the card or when you have the SD card interfaced to your computer.