Coming from a cycling background, IDPA is WAY safer.
At any given day of bike races, there were usually about 200 or so people competing in 8 to 10 events. On average, 15 to 20 people crashed at some point and got bruised and cut. One or two would be bad enough to warrant an ambulance ride to the hospital.
In the dozen or so IDPA matches I've been to, I've yet to see anyone bleeding and no one went away in an ambulance. True, it's an individual sport instead of a group sport at high speed and close quarters, but it does not change the number of injuries involved.