Welcome. I've read that both groups regarded the other as occasionally over the top in some fashion or another. The Outfit seemed to be more willing to use torture. Also in the Midwest car bombs were more common (though this was not all The Outfit)

I'm not familiar with any personal animosity between Accardo and Bonanno outside of the Chicago Outfit's wariness about Bonnano's attempted expansion into Arizona and other places which the Outfit already had a foothold.

"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming

Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.