Only in venue; not necessarily in result. The latter is using the "BatPhone" to call "Wayne Manor"; the former can be a more informal, less immediate attempt to wield persuasion over which type of "archFreeperfiend" the BatModerator should monitor on his BatCaveScreen.
When the abuse button is used, ALL of the moderators are notified. If I am not around, they will use their best judgment to deal with the complaint.
Ironman can beat the pants off Batman.
(but I like your analogy)