I have three coins with CAC stickers in my Type Set. They're all very appealing. Each of them does seem to have a special something - something you can point to and say "that's why it got the sticker." I had very little idea what, if anything, the sticker was supposed to imply. I just guessed a CAC sticker was kind of like an NGC star: It indicated especially striking eye appeal. But I went to their website today and their statements about what they do seem almost to emphasize that that is NOT what they are.
I'm obviously paraphrasing here and certainly may have misunderstood any or all of what I was reading, but anyway: They say they imagine an accurately graded coin in three levels 1. Spectacular for the grade. 2. A solid example of a coin in that grade (presumably with no distractions or reasons for doubt), and 3. A coin that may or may arguably deserve the grade assigned, they are ordinary in every way. They say that they will give coins of the first two descriptions the shiny green stickers, and return the others un-stickered. They also provide the number of coins they've examined and the number that got stickers. It looked to be roughly 2/3 got stickered.
I don't have the money to lavish on it at this time, but I have a lot of coins I think would get stickers. (Ideally that should be ALL my coins, but alas, sometimes I just made a dumb decision.) I'm tempted to try it, just to see how their judgement compares with mine. That's also, incidentally, the main reason I send a coin to be graded in the first place, on the occasions I've done that.