I don't think players are using consume for the HCI.
Inspire: Party Hit chance increase by up to 15%, Damage increase by up to 40%, SDI increased by up to 15% (PvP Cap 15)(Provocation Based)
We do not know how much HCI can increase with consume.
Inspire also gives damage increase. But, does the damage increase work on toons that have 100 DI?
IMO Inspire is better. Works on Beacons and includes all close by party members.