As you suggest, you can skip the date check as that can be changed without the contents changing.
First check that the sizes are different. If so, that may be enough to conclude that they are different. This can have false positives too though depending on the types of files. For example a unicode text file may contain the exact same content as an ansi text file, but be encoded with two bytes per character. If it's a script, it would execute with exactly the same results, but be twice the size.
If the sizes are the same, they may still contain different bytes. The brute force test would be to load each file into a string and compare them for equality. If they are big files and you don't want to read them all into memory if not necessary, then read them line by line until you encounter a difference. That's assuming they are text files. If they aren't text files, you can do something similar by reading them in fixed size chunks and comparing those.
Another option would be to to run the "fc" file compare command on the two files and capture the result and do your update based on that.