If file sizes match just compare hashes (Digest::MD5, Digest::MurmurHash).

I don't know anything about MurmurHash, but MD5 has a higher chance of collisions than more modern hash digests. While, in all likelihood, this will not be a problem for this kind of usage, i would still go the recommended path of using something like SHA256 or even better SHA3-512.

See also:

• https://en.wikipedia.org/wiki/Secure_Hash_Algorithms
• https://metacpan.org/pod/Digest::SHA3
• https://en.wikipedia.org/wiki/MD5#Collision_vulnerabilities