Both are more interesting versions of eating a regular old soft chocolate chip cookie (we recommend finding someone's grandma to make you them), but one Chips Ahoy! has too much icing flavor while the other doesn't have enough.
Our recommendation is to buy both, and eat half an Oreo crème filled and half a birthday frosting cookie to achieve pillowy, chewy perfection.
Lee Breslouer writes about food and drink for Thrillist, and doesn't know the difference between frosting and icing, probably because they're the same thing. Follow him at @LeeBreslouer, because you can't make up a name that good.