I've stayed in both... Fairmont last summer and Valley Wing a few years ago. The Fairmont has a more convenient and centralized location, and sits atop a large shopping mall, across the street from Raffles, etc. Rooms are fine though a little dated.
The Shangri-la is more elegant and grander, with much nicer grounds and pool, though it is farther away and a good walk to Orchard Row. But the Valley Wing is the best... we were upgraded as Golden Circle members and it was awesome; much nicer room... as one of the staff said: "you are kings and queens". Breakfast, afternoon champagne and appetizers, etc. made it special. And staff were very attentive.
Enjoy Singapore!