There are a couple of major benefits and disadvantages to both the counter depth and standard depth refrigerators.
Counter depth gives you the clean and flush look in the kitchen by having just the door stick out past your counter tops where as a standard depth will stick out 6 to 10 inches beyond the counter top.
Counter depth still offer all of the same features and benefits as a standard depth fridge but you lose out on capacity. This is the major disadvantage as an average standard depth refrigerator is between 26 and 30 cubic feet while a counter depth refrigerator varies between 19 and 24 cubic feet.
Another disadvantage is the price of the counter depth refrigerator. On average you tend to pay more for one than a standard depth because it is considered a specialty appliance.
In the end if you prefer to have a clean look over a larger capacity then counter depth is right for you.