There's some irony there given that excessive body-scanning and hyper-vigilance can be common symptoms related to anxiety.
Though the CBT stuff in general and being aware of your attention does seem empirically helpful, I just find the body scanning focus as a common start may not be the best.
The primary difference is that the kind of awareness cultivated during meditation is non-judgemental. Mindfulness helps put thoughts into perspective, where you can observe them rather than feel absorbed by them. So in this sense you can pay attention to your body without getting carried away by the stream of anxious thoughts.
And therein lies the difficulty of the process: shifting towards objectivity, in a sentient being that is primarily (if not entirely) a subjective experience. I appreciate CBT, but often feel saddened to see that this doesn't get addressed in most of the resources attempting to educate about the practice.
"Mindfulness and psychotherapy" (by Germer, Siegel, Fulton) has helped me with these issues by giving multiple perspectives on the process to develop. It's a book for therapists, which is one of its strengths, since we essentially are trying to get people to sustain being their own therapists in the long run.
Though the CBT stuff in general and being aware of your attention does seem empirically helpful, I just find the body scanning focus as a common start may not be the best.