Cross-country skiing in Livigno has a concrete advantage you might not hear mentioned often: you can literally start whenever you want during the season, because you don't depend on slope conditions like alpine skiing does. If a week goes by without fresh snow, the ski lifts stay open anyway for cross-country, so you have more flexibility to follow courses without missing lessons.
My practical advice I'd give you, though, is this: go watch both courses in action live once, even if just for an afternoon. It's not as simple as it sounds. You'll see how beginners move in alpine skiing (spoiler: you'll see a lot of them sitting on the ground) and how cross-country skiers instead maintain their posture even when they mess up. I think it changes how you perceive what "feels" easier to you. In cross-country you feel your body's movement as it glides, it's almost meditative in a way if you're not in a rush to throw yourself down a mountain. Alpine skiing, on the other hand, is more of a nervous-motor shock at first, regardless of what others say about technical difficulty.
I'd only add that in Livigno specifically the two are almost separated geographically - cross-country is in the valley floor, alpine is on higher and steeper slopes. If you choose cross-country, you start breathing well right away and get to enjoy the landscape. If you choose alpine, you have fun but those first days you burn a lot of energy just staying on your feet. Nothing tragic, just a matter of what state of mind you want to have after the course.