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> I wonder if skyiing is safer with respect to head injures.

The answer is: it depends. Friend of mine got pretty badly concussed skiing a blue run (easy) without a helmet.

I've done both skiing and snowboarding, always wearing a helmet for both after similarly hitting my head on day 3 of snowboarding (though without the concussion). Plenty of falls on both but I've hit my head a lot less frequently skiing than snowboarding. Still, it can happen and, realistically, it only needs to happen once for you to experience life changing injuries.

Wear a helmet, always, regardless of whether you're skiing or snowboarding. And don't screw anything to it or be tempted to wear a camera attached to it (GoPro, Garmin, etc.).