The only similarity between CD and Atkins is the ketosis thing, which doesn't mean a lot anyway
I don't think Atkins is particularly unhealthy. As Lostris says, it depends how you do it. The low-fat brigade will say it is and probably produce evidence, and the high-fat brigade will say it isn't and also produce evidence
Weight-wise, obviously cambridge is quicker. You will lose weight if you do the diet. With Atkins it's a little more to do with what you eat. Remember that it's reduced calories that reduce the weight...nothing to do with carbs.
CD is a short term plan. Follow the plans up and you will be out of ketosis and have a similar glycogen load as the average Joe bloggs down the road.
Atkins dieters, are encouraged to stay on the plan for life, though of course, for maintenance, the would be eating more carbs, but probably less than good old Joe Bloggs.
Personally, though I've done the Atkins diet on a number of occasions, these days I tend to favour moderation in all food groups, so I wouldn't do it for that reason. I also wanted a plan that would encourage me to come safely back to some form of normality and give me the confidence to live again without a 'diet' as such. Cambridge are one of the very few diets that could give me that.