On my recent BG we went via the Hause and then took a line up and down the grass on the right of the wall as you look up Fairfield from the col, this avoids the horrible scree slopes/path. The other line commonly used goes to the left of the blue line on Bob's photo; you follow the small stream up about 100m and then the path goes leftwards, and then straight up to come out just below the little rock steps on the path betwen St. Sunday and Fairfield.
I think that there is little time difference in whatever way you go and what is more important is saving energy and having a way that you are happy with.