Safety comparison, downhill mountain bike vs. downhill ski
Having done both, I'd say they are about equally dangerous with the edge going to downhill biking.  

It's easier to gain momentum on a downhill bike and harder to properly lose it.  Additionally equipment failure is a bigger concern and generally more catastrophic.  Downhill biking in the winter pads the ground (like skiing) but, during all seasons, trees are an ever present danger.  Losing control and hitting an unmoving object at 30 mph will generally have a bad outcome.  

As a parent myself, I expect I'll probably downhill bike with my children at some point. As long as they work on learning control at slower speeds first and learn how fast and hard to press their limits they'll probably be fine.  Most of the injuries I have seen downhill biking have been with younger kids trying to ride way above their ability level.  The group of older guys I ride with are rarely (if ever) injured.  We generally ride right at our ability level and maintain control.  That being said, none of us are ever going pro.

In your situation, if you are just trying to maintain consistency AND have already decided downhill skiing is out (based solely on risk) then I'd say you should probably exclude downhill biking as well.