Ultrasound dating. First trimester ultrasound is accurate within 5-7 days. There is no test that can date conception more accurately than a 1 week window.
Ultrasound +/- 8% Properly performed and interpreted ultrasound examinations have a variability of 8% plus or minus the measured dating. Given the dates in the question and assuming a high-quality ultrasound, i would suspect that last menses dating is inaccurate. Ultrasound dating at 6 weeks 0 days should have a 95% confidence range of 5 weeks 4 days to 6 weeks 3 days which is +/- 8%.
Less likely. Ultrasounds done early in the pregnancy are very accurate. It's unlikely that it would be off by a week in most cases, but it is not universal since mistakes or misreads happen. Also, one week is not a big variation after all. A subsequent ultrasound in a few weeks might be able to further establish your due date in a more accurate manner.