There was an acknowledgement of the situation by Batman, at least—although I am afraid I cannot locate the comic. It was probably when the two characters crossed over for the first time, in the 1940s or 1950s.
According to Wikipedia, the similarity between the heroes in Green Arrow's earliest days was practically comical:
He retooled the concept into a superhero archer with obvious Batman influences.
These include Green Arrow's sidekick Speedy, his use of an Arrowcar and Arrow-Plane for transportation, his use of an Arrow-Cave as his headquarters, his alter ego as a wealthy playboy, the use of an Arrow-Signal to summon him, as well as a clown-like arch foe named Bull's Eye, similar to Batman's arch-foe, the Joker.
When they met, Batman asked Green Arrow something to the effect of: Don't you have any original ideas? Unfortunately, I do not recall Green Arrow's response, nor can I locate the comic in which this occurred. Unlike the first Batman-Superman crossover in Superman no. 76, it was probably not extensively reprinted (although I must have seen it in a reprint somewhere).