How can I check if rsync made any changes in bash?

Based on the comments to my original question, make rsync output to stdout with the -i flag and use a non string check condition to see if anything actually changed within the error code check. Wrapping the rsync command in a variable allows the check to be done.

RSYNC_COMMAND=$(rsync -aEim --delete /path/to/remote/ /path/to/local/)

    if [ $? -eq 0 ]; then
        # Success do some more work!

        if [ -n "${RSYNC_COMMAND}" ]; then
            # Stuff to run, because rsync has changes
        else
            # No changes were made by rsync
        fi
    else
        # Something went wrong!
        exit 1
    fi

Potential downside, you have to lose the verbose output, but you can always log it to a file instead.

I wanted a more strict solution. I don't want to grep for Number of created files: (the message could be in another language) or remove all lines but two in -v output (who knows what summary rsync will print in the next version?).

I found that you can set the format of a rsync's log, but not the format of its stdout (see man rsyncd.conf).

For example, add a "File changed!" to each line with an actually changed file, and then grep for it:

rsync -a \
    --log-file=/tmp/rsync.log \
    --log-file-format="File changed! %f %i" \
    source-dir target-dir

if fgrep "File changed!" /tmp/rsync.log > /dev/null; then
    echo "rsync did something!"
fi