Any check of whether the file changed or not would be pointless, since you gotta find out what changed anyways.
You might as well go right away and scan the file for the changes.

Code:
alias txt_crc {
  var %file1 = <enter filename here>
  var %file2 = Backup.txt
  var %i = 1
  while %i <= $lines(%file) {
    if $read(%file1,%i) != $read(%file2,%i) {
      write $+(-l,%i) %file2 $read(%file1,%i)
      .msg <channel> $read(file1,%i)
    }
    inc %i
  }
}


This alias can be triggered manually, or used with a timer.
A note on this is that this check can take a while if the file is long!
If you set it to run every couple of seconds, be ready for mIRC getting frozen.

Good luck,
ziv.