Skinning - good for cooking methods that involve moisture (baking in a sauce, soup, boiling, pressure cooking, crock-pot)
Plucking - good for cooking methods that involve direct heat (grilling, roasting, pan-frying)
If you try to roast a skinned bird, the meat will dry out. You'll need to cover it with foil or a lid to keep the moisture in.
Also sort of depends on the age of the bird in question - an older cockerel or hen will do better with a 'low and slow' cooking method rather than 'high and hot' - so an old bird needs a slow roast, a young cockerel can take a hot grill.
In terms of processing, yes, skinning is much like trying to take a jacket off an infant. We personally skin all our chickens. Why? Because of time. We can process more in x given amount of time than trying to pluck 'em.
CX don't really have that many feathers overall, so plucking them by hand is easier than say a dual-purpose bird or a Ranger type broiler bird. Trust me, we've grown both! So, ultimately, the choice is yours. Try each way and see what works for you. And your style of cooking. If you want luscious fried chicken, you'll need the skin on. If you want chicken n' dumplings, you won't need the skin. Depends on what you'd like to do with the meat overall.