Neither are particularly great on Volibear. As a general rule of thumb, if you don't have spammable AoE physical damage abilities BC is not a good buy. Frozen Mallet is an alright item on Volibear when your team desperately needs more crowd control. Otherwise a nice amount of CDR and Majestic Roar fulfills Volibear's CC needs.
Volibear gains damage while building health and his ultimate does a terrific amount of damage over time by itself. If you're hell bent on giving Volibear a damage item, then on-hit attack speed items (BotRK, Wit's End, Statik Shiv) are a solid way to go. His own attack speed steroid on W means more on-hit damage procs from the item, and the items' attack speed means more procs of his ult over its duration.