How accurate is this website?

The ARWU rankings are based on measurements of research productivity and faculty distinction.
The USNWR department rankings are based on peer assessments (opinion polls of college professors/administrators). Whether one or the other is a better reflection of graduate program quality is hard to say.

Here’s yet another physics program ranking, in case you’re interested:
http://chronicle.com/article/NRC-Rankings-Overview-Physics/124754/