Statistics show that skiers are 3 times more likely to be involved in a collision than snowboarders.
Dr. Shealy's research also confirmed that alpine skiers are three times more likely to be involved in a collision with other people than snowboarders.
http://www.nsaa.org/nsaa/press/facts-ski-snbd-safety.asp
This article makes interesting reading, it says, among other things, that the risk of collisions has stayed fairly static over the last 30 years.
I have also seen research (but cannot find it now) that showed that skiers are more likely to collide with other skiers and snowboarders are more likely to collide with other snowboarders.