In theory, body ("boogie") boards would seem safer...softer, closer to the water.  Not necessarily as they are slow, necessitating a late take off which can lead to separation of the board from the water.  In the first frame, note the body board is already about a foot off the water, and the body boarder is preparing for a 10' freefall, with predictable consequences.


Body boarder doing everything to not go over the falls