Rsync doesn’t skip existing files

There are 2 parts to this question. First, why is there a difference between "Number of files" and "Number of files transferred". This is explained in the rsync manpage:

Number of files: is the count of all "files" (in the generic sense), which includes directories, symlinks, etc.

Number of files transferred: is the count of normal files that were updated via rsync’s delta-transfer algorithm, which does not include created dirs, symlinks, etc.

The difference here should be equal to the total amount of directories, symnlinks, other special files. Those were not "transferred" but just re-created.

Now for the second part, why is there a size difference with du. du shows the amount of disk space used by a file, not the size of the file. The same file can take up a different amount of disk space, if for example the filesystems blocksizes differ.

If you are still worried about data integrity, a easy way to be sure is to created hashes for all your files and compare:

( cd /home/hholtmann && find . -type f -exec md5sum {} \; ) > /tmp/hholtmann.md5sum
( cd /media/wd750/c51/home/ && md5sum -c /tmp/hholtmann.md5sum )

I suspect that the length of this directory/path is the issue. You could test this theory by trying to run these commands:

$ mkdir -p /media/apb/0543d632-d24b-4b4e-8ca8-56d22c19e62f/backintime/myhost.mydomain.com/root/4/new_snapshot/backup/home/apb/Documents/7uzyrwsy.default-20131026-1639/Mail/pop-server.bak.rr-8.com/
$ touch /media/apb/0543d632-d24b-4b4e-8ca8-56d22c19e62f/backintime/myhost.mydomain.com/root/4/new_snapshot/backup/home/apb/Documents/7uzyrwsy.default-20131026-1639/Mail/pop-server.bak.rr-8.com/.Sent.msf.RZMdLy

The first will attempt to make the directory tree, the second will touch the resulting file in this directory.