It's really only the first days/weeks of snowboarding that you're likely to fall often. Mostly, you need to have an instructor and pick the suitable terrain and snow conditions for a beginner. Really, it's not that hard.
I've also noticed that for an intermediate snowboarder, it's quite easy to go through steep/bumpy slopes or powder where intermediate skiers struggle. But you're usually faster on skis.
That being said, if I could go back in time and learn skiing instead of snowboarding, I would. It's more versatile, and I think less demanding on the body overall (in particular, snowboarding is asymmetrical which I think puts extra burden on your neck.).
Skiing deep powder is a ton of fun. My snowboard friends constantly worry about getting stuck in deep powder with their boots buried and no easy way to unbind. If they fall they end up doing the worm until they can bring their board to the surface.
Probably only a concern on low angle stuff, but yeah, one weekend I was repeating this traverse in the trees, trying to only lose like 20 feet over a longer distance, and it became very like, low speed technical. Take two nice powder turns, then head between those two trees, stay in existing tracks, duck branches and just try and make it so you don't have to unstrap and hike to the next incline. Skiers can definitely manage that better.
If you fall on the board you roll over and come up again and keep going. On the skis you lose the skis to the right and left and get a spiral fracture of your legs and a hip join breaks off :)
I've also noticed that for an intermediate snowboarder, it's quite easy to go through steep/bumpy slopes or powder where intermediate skiers struggle. But you're usually faster on skis.
That being said, if I could go back in time and learn skiing instead of snowboarding, I would. It's more versatile, and I think less demanding on the body overall (in particular, snowboarding is asymmetrical which I think puts extra burden on your neck.).