Example:
Maybe it's the old story, maybe he just sees me as a friend.
Maybe it's the same old story, maybe he just sees me as a friend.
Which version is more commonly used by native speakers of English in cases like this?
The sentences have different meanings. Each is correct but with a different meaning, so usage statistics is quite pointless. Which is more often used: "I love you" or "I hate you"? Pointless question.
In the first sentence, the speaker would wish a closer relationship, but as has happened to many other people in history before, the other person just wants friendship.
In the second sentence, the speaker would wish a closer relationship, but as has happened to the speaker many times before, the other person just wants friendship, and the speaker is not happy about it.
"the same old story" is an idiom for an experience that we make repeatedly, and that we find tedious. "the old story" is a much less strong idiom, and it doesn't have the connotation of dislike with it.