Both Courage and Rooster are charismatic outsiders who inspire loyalty bordering on devotion, despite their oft-expressed cynicism and self-interest. Both have a strong hedonistic streak and refuse to compromise. And both, in many ways, are victims of mainstream society who could easily be pitied.
I suppose these characters might be called antiheroes - they certainly have things in common with characters in this list (which, fabulously, includes Arthur Dent). But I also like the term 'Machiavel' (derived from Machiavelli) that I found recently in Jonathan Bate's book about Shakespeare, Soul Of The Age.
In Elizabethan times, Bate explains, Machiavelli's writings were widely demonised and a writer like Marlowe only gave voice to them in patently 'evil' characters.
Shakespeare, however, while 'recognising the theatrical charsima of the Marlovian Machiavel', makes them real characters with real motivations. Characters like Richard III, Iago and Edmund in King Lear who 'say the unsayable' and challenge conventional thinking.
That's what Courage and Rooster do, too. And like, Shakespeare's characters, though appearing to be completely cyncial, deep down they are in fact supremely principled.
That's why they break our hearts.