Well there aren't any real benefits to registering your dog unless you might ever want to show/breed. As for the differences between AKC and CKC well, night and day. AKC you are getting a guaranteed purebred dog with a traceable history. CKC means absolutely nothing since anyone can get CKC papers on any dog. I would just as soon not have any papers as have a so-called registration from the CKC. It's like the people who advertize their kennels are USDA. Well that's great, it means the kennels are clean and pass health inspections but that's all. I guess that also means they probably aren't a puppy mill at least.
When you register a puppy or dog under CKC you have to send in pictures of the dog, that include, right shot, left shot, and front view, (full body) so that the people that issue the papers can most likely tell if the dog is mixed or not, but AKC pretty much guarentes it