Check out
this photo set for many examples of how not to ride the sand.
This race (in the photos) featured a long stretch of deep sand going down to the beach, a longer stretch across the beach and the a long stretch back uphill to the grass. Obviously wet, packed sand is great for riding so the beach part itself was nice. Everyone ran the uphill sand. I saw a few people who somehow shot down through the downhill section like it wasn't even slowing them down. I don't know how they did that -- maybe it was luck. Mostly, the people who rode it either fell spectacularly (usually immediately on entry from the grass) or churned slowly through it at about the same pace as the people running it or possibly a little slower.
Two observations:
1. The runners never fell. The riders fell often. On average, I think this gives running a big bonus.
2. When running, you can actually pick your line and come out of the sand where you want. When riding, you go where the sand takes you. BF member aggiegrads gained a bit of an advantage by finding a place where the sand firmed up early and let him remount sooner than most of his nemeses. I missed that trick but still felt like running let me line up well with the firmest parts of the beach.
Of course, that's somewhat specific to this particular sand configuration. I've done races in the past that went through sand traps on an old golf course or inland beach volleyball courts and with the short stretch of sand riding was definitely faster than running, even after you factor in the risk of falling.