Using diff with the recursive -r and quick -q option. It is the best and by far the fastest way to do this.
diff -r -q /path/to/dir1 /path/to/dir2
It won’t tell you what the differences are (remove the -q option to see that), but it will very quickly tell you if all the files are the same.
If it shows no output, all the files are the same, otherwise it will list the files that are different.