Group wildcard = looks for any new talkgroup on the trunked system
Private wildcard = looks for any new radio to radio "private call" on the trunked system
Depends on where you are and which system you are listening to, but I only use the talkgroup wildcard. For me, it is used to discover new talkgroups. The only caveat is you have to enter and lockout all of the unwanted talkgroups so they don't show up. Some systems allow private calls, which is radio to radio only communications, some do selectively (between supervisors), and others don't allow them at all.
Your mileage may vary, but I do use Group wildcards on every trunked system I monitor.