Not sure about accuracy, first month I got my S3, phone said I used a little over 10GB, verizon bill said I used just under 6gb.
Strange thing is, up until the day before the bill, the verizon online useage estimate shows same exact amount used as what my phone said. But some how when the bill came, it was much lower.
Same thing happes on my galaxy nexus on verizon. Up until the day the cycle ends, the online estimate almost exactly matches what the phone shows for data used. but the bills are always lower.