Many people find it easier to maintain control on a board than skis, particularly at high speeds and on ice. Novice snowboarders cut people off and flail around, just like beginning skiers. The difference is that skiers remain at the novice level for a much longer time period. Fast does not mean uncontrolled, and a crucial lesson in riding is to lose the fear of speed, because it's harder to handle steep slopes or challenging terrain if you're trying to check your speed or turn too much. Well, maybe if you fell off a cliff or something, but I doubt it.
Studies show that skiing causes a much higher percentage of knee injuries than boarding.
Snowboarding entails a higher risk of thumb and wrist damage, but most serious falls result from attempting jumps and tricks. If you feel timid, just freeride instead. I just feel bad that they're missing out on the superior winter sport. Hopefully I'll see some of you converts out there this winter. And if you see a crazed looking guy snowboarding in a black leather jacket and army pants, don't laugh too hard, that's our editor.