If your kids are 13 or older, I'd recommend getting both. Once they're 18, the passport card could be used as their form of ID to fly within the US, and just as an official US ID. Not all kids who turn 18 have drivers licenses. We got our first set of passports in 2016, when my oldest turned 16...I wish I got her both...she's 18 now and her passport book is her only form of official ID. (I don't want to pay for a state id and then have to pay for the drivers license...she has a learner's permit...with 11 months left on it...ug)
But to answer the question, if you needed to fly from another country (even in an emergency situation), everyone needs the passport book. If you're just going to another country by land or sea, a passport card will work.