I don't know about cross country skiing, but if we're talking about winter mountaineering, skis > snowshoes.
Snowshoes are easier to start with, simpler and a lot cheaper.
Skis are way faster, generally provide more lift, are easier to traverse a slope with, and -this is the winner- you can ski down again.
They are a lot more expensive, you'll need boots, skis, skins and special bindings. And if you want to ascend slopes that are steeper than 25-30°, you'll have to do kick turns, (usually much shallower) whereas snowshoes will take you straight up. But >30° is avalanche terrain anyway, so more often than not you stay away.
And you need to learn about how to treat skins, wax, etc.
But it's all worth it, because you can ski downhill. Have I mentioned that you don't have to walk down? Because you don't. You ski.
