Before the Crisis on Infinite Earths, there were Earth 2 (the home world of the Justice Society, and their versions of Batman, Superman, and Wonder Woman), Earth 1 (the more important stories happened there for the longest while, since the 60s to early of the second half of the 80s).
And then came the Crisis, and there was a New Earth, molding together different versions of existing characters, and some of them were reinvented.
I don't know about Wonder Woman, but when it comes to Superman it is very easy to tell the difference between Earth 2 version, Earth 1 version, and Post Crisis version.
Earth 2 Superman worked at the Daily Star, he was never Superboy, his logo is simple looking, he married Lois Lane, and we saw him age and the silver lining in his hair surfaced, not to forget his cousin Kara is Power Girl and not Supergirl, he even had some adventures teaming-up with Superman of Earth 1.
Superman of Earth 1 never married, his logo looks more sophisticated, and he was responsible for the deaths of Martha and Jonathan Kent during his days as Superboy.
Superman post Crisis had a complete retooling of his origin, an aura protecting his skin tight outfit, nothing protecting his cape from being shredded because it is made from Earth cloth, and his adult form still visits Martha and Jonathan Kent. Although this version of Superman retains some of the Earth 1 Superman memories from the Crisis on Infinite Earths, there was a story starting in Superman v2 #008 displaying some of the various differences between Earth 1 Superman and post Crisis Superman.
When it comes to the different versions of the villains, it remains easy to tell the difference between different versions of the character, because of the various takes on the villains, like Lex Luthor and Metallo.
Batman -on the other hand- has a story working like an interwoven threads, some issues like Batman #300 offer the different version of Batman, but in that issue the narration presents it as an alternate future for the same Batman from the Justice League, not the Justice society version of Batman.
In the story running in Detective Comics 471-472 Steve Englehart brings note to a Golden Age story, stating it happened in the past of the pre-crisis Justice League version of Batman, and plays like there is no different version of two different Earths.
In the post crisis era there is one notable point distinguishing that version of Batman from Earth 1 Batman, the story of Jason Todd, and his introduction as the second Robin.
In Crisis on Infinite Earths, Huntress explains Earth 2 Batman passed away, reminding readers that there are two different versions of Batman before the Crisis.
In one of the Grant Morrison issues before Flashpoint, Jason Todd is revealed to have red hair, and he is the pre-crisis version.
How can one separate stories between the different takes of Batman? How can one tell which story is supposed to represent which version of the character?