Crunches mainly target the superficial muscles and don't hit the deeper transverse abdominus muscle, the «girdle» muscle that holds everything in. (cathe.com)
In contrast, planks work multiple muscle groups, including the internal obliques, the deep transverse abdominus, and the stabilizing muscles in your hips and back. (cathe.com)
A quick note: I have not listed any abdominal exercises lying on your back as my favorites for working transverses abdominus because it is hard to not let your rectus abdominus take over in a crunch position. (hab-it.com)