(Following, compliments of Laura Beth Kupperman)

No. It's fairly even, skiers and boarders have about the same number of injuries but those injuries are different. You are much less likely to sustain knee injuries while snowboarding than skiing. There has been a recent study on snowboarding injuries. The study was done in Australia and appears in "The American Journal of Sports Medicine" vol. 21, no. 5, pp. 701-704. In this article comparisons between skiing and boarding injuries are documented for a 4 year period. The distilled info goes something like this: skiers are much more likely to injure their knees, and when they do injure their knees the injury is usually worse (grade II or III, if that means anything to you) than a boarder's knee injury (usually only grade I or II, with only one grade III reported during the course of the study). Boarders are more likely to injure their ankles, feet, wrists, and hands. There is also info in the article about soft boot injuries vs. hard boot injuries. The study aside, though, you can pretty much understand just from looking at a board why there are fewer knee injuries. When you fall you pretty much either go straight back on your bum, or straight forward on both knees (or hands if you stick them out (hence the increased # of wrist injuries). It is really hard to torque your knee when your feet remain locked in place.

(Following, compliments of Surfdog789)

After seeing Dave Schutz bibliography, I checked out Medline for more articles. The abstract (summary) that follows is interesting [from Am J Sports Med (US), Sep-Oct 1993, 21 (5) p701-4]:

"Information on the rate and spectrum of snowboarding injuries is limited. This 4-year prospective study at 3 major Australian ski resorts assesses incidence and patterns of snowboarding injuries, particularly in relation to skill level and footwear. Ski injury data were collected for the same period. In a predominantly male study population (men:women,3:1) 276 snowboarding injuries were reported; 58% occurred in novices. 57% of injuries were in the lower limbs, 30% in the upper limbs. The most common injuries were sprains (53%), fractures (24%), and contusions (12%). Comparing skiers' versus snowboarders' injuries, snowboarders had more fractures to the upper limbs, fewer knee injuries, and more ankle injuries. Ankle injuries were more common with soft boots..... Knee injuries and distal tibial injuries were more common with hard boots... Overall, novices had more upper limb fractures and knee injuries; intermediate and advanced riders had more ankle injuries. Falls were the principal mode of injury. To prevent injury, beginners should use soft boots and take lessons."

All I can say is - never mind the danger, just think of the fun!