I do both and when the closest groomed trail is packed enough to be rideable without ruining it for the skiers, I'm faster on the bike.

My best time going up on the bike in the winter is 3.9 miles in 41 minutes. My best time on classic skis is 56 minutes. On skate skis it's probably about 50 minutes but I don't recall ever actually keeping track. Once I turn around and go back down the difference is more pronounced but I don't push it. There's too much traffic. One skier in the wrong place at the wrong time with me bombing it at a 16-18 minute pace is bad news.

I've been xc skiing for over 10 years. I'm more of a backcountry guy instead of a skate skier though. Given some refinement in my technique I might be able to threaten the bike going up but I don't see how I could average 15 mph in more than a few sections coming down.