Assuming the hacker has access to the ciphers of each of the versions, will it help him/her to decipher the original file(s) by doing some sort of comparison of the ciphers?
For modern ciphers when well-implemented, no: encrypting different versions of the same plaintext(s) with the same key does not make the cipher attackable.
That's because adversaries having access to nearly the same data encrypted multiple times is part of what's assumed in the baseline attack model for all modern ciphers: Choosen Plaintext Attack. The cipher is nearly never the weak link in the security chain. That's true including for AES-CTR.
Problems do occur when the random generator used for the Initialization Vector fails, or is omitted; indeed CTR mode is sensitive to that.
To a lesser degree, some side-channel attacks could be facilitated by multiple slightly different plaintexts.
Knowing that all the files are the same would fall in terms of difficulty between a ciphertext only attack and a known plaintext attack. In the ciphertext only attack, the hacker knows the ciphertext of each file/message and nothing else. For a known plaintext attack, the hacker knows the contents (plaintext) of each file (even if those contents are different for each file) as well as the ciphertext. So your attack would be easier (for the hacker) than a ciphertext only attack, but not as easy as a known plaintext attack.
Both of these attacks (and some others) are considered when designing a modern cryptosystem, so any cryptosystem that is vulnerable to a either attack (when properly used - reusing a nonce is typically forbidden) would be considered broken.