Just use rsync -va
NO STOP!
The default quick check algorithm of rsync is not safe for this. It only checks filesize and modification time to determine if files are equal. After a b0rked copy, these are not to be trusted.
You should add the -c flag so that files are properly checksummed, unfortunately if you have slow storage on either end, this often negates the speed advantage of rsync.
For example, consider this example:
mkdir source
mkdir destination
echo "hello" > source/file.txt
echo "world" > destination/file.txt
touch -r source/file.txt destination/file.txt
rsync -avh source/ destination/
cat source/file.txt
cat destination/file.txt
Contrary to what you might expect, the rsync command copies nothing and the output at the end will show:
hello
world
If you change the rsync command in the example above to rsync -c -avh source/ destination/, it will work as expected.