COBRA charges the same premium as the group insurance you had with your employer, perhaps with a small surcharge tacked on. It's more out of your pocket simply because your employer isn't pitching in anymore.
If you're young and healthy, COBRA may cost more, since it's a rate for a group that probably includes older and sicker people. You're healthier than the average person in the group so individual insurance is cheaper.
But if you're older or sicker yourself, going with individual insurance means you no longer have those healthy young people propping up your insurer's profits, so you'll pay more with individual insurance. A friend of mine was charged quite a bit more, and wasn't even especially unhealthy.
Of course all this will change at the beginning of 2014.