It would depend on who gets there first like someone said previously. But an Ordo Malleus would obviously have more expertise and resources when dealing with the demonic. All of the Ordos have equal authority and jurisdiction but certain Ordos are more specialized in dealing with certain things. A Ordo Sicarius Inquisitor holds the same power as a Witch-Hunter or Daemonhunter but wouldn't necessarily have specialized resources like daemonhosts, wards, etc. and would be more suited to investigating or carrying out assassinations.
"You do not need to look to the stars to find the greatest obstacle this Conclave faces, my brothers. Simply gaze around this room and you will find such a sea of discord as to make your foes cackle with glee." - Inquisitor Eistus Gracker in address to the Calixian Conclave
"There are dark pitted corners of our universe that have bred the most unfathomable horrors and blasphemies that would burn and blind the sanest man. Fortunately sanity has never been a prerequisite of membership in the Holy Ordos." - Inquisitor Silas Marr