I would expect the file access time to dominate everything else, so choice of hash won't matter too much.

You could try benchmarking different ones to see, maybe sha256 & md5?

There was an interesting thread at high speed checksum for video finger printing?. You could possibly use a similar technique for your larger files, but you've still got to read it off the disk.

OTOH you could just use rsync and go get a coffee :)