Responses
It wasn't mention that being part of the 3 Greats means the strongest. They qualified for some criterias, just like the 13 crowns, to be called the 3 greats. Of course, their strength is not to be disregard since they're all Rank Yod (10), except Sullivan who's Rank 9, which is by choice. As per the story the 3 heroes is less or on par with the 3 greats. That's why it is a bloody battle.
They are not afraid strengthwise, they are afraid of the impact of Pres Barbatos' anger. The disruption that it would cause.
I thought that the three greats are the most powerful and respected in the underworld after the demon king, so why are they afraid of the Bachiko clan or the three heroes family?