I have always used the 1st way, w/my pick parallel to the strings. I think it produces a much fatter, warmer sound this way. Approaching the string w/the edge of the pick can produce a harsh sound, especially if your playing w/a clean tone.
The one thing I noticed he doesn't make light of is alternate picking. If you have the pick angled 45 degrees for the down pick your gonna have to angle it 45 degrees in the opposite direction for the up-pick. A lot of players who use the circular picking method w/the fingers do this. I don't recommend using this method, you are relying on the finger muscles for the majority of the work,wich are very small and weak.