Problem mit passwortfreiem SSH SLES12

Hallo,
ich habe folgendes Problem: ich möchte, dass 2 SLES12 Server per rsync gegenseitig passwortfrei Dateien austauschen können. Bei dem einen hat es problemlos funktioniert:
ssh-keygen -t rsa
Generating public/private rsa key pair.
Enter file in which to save the key (/home/willi/.ssh/id_rsa):
willi@server1:~> ssh-copy-id -i ~/.ssh/id_rsa.pub willi@server2
The authenticity of host ‚server2 (xxx.xx.xx.xx)‘ can’t be established.
ECDSA key fingerprint is 96:a0:9f:7d:1b:c0:99:85:ab:d8:d7:e3:78:27:91:5e [MD5].
Are you sure you want to continue connecting (yes/no)? yes
/usr/bin/ssh-copy-id: INFO: attempting to log in with the new key(s), to filter out any that are already installed
/usr/bin/ssh-copy-id: INFO: 1 key(s) remain to be installed – if you are prompt ed now it is to install the new keys
Password:

Number of key(s) added: 1

Now try logging into the machine, with: „ssh ‚willi@server2‘“
and check to make sure that only the key(s) you wanted were added.

willi@server1:~> ssh server2
willi@server2:~> exit

Umgekehrt funktioniert es nicht:
ssh-keygen -t rsa
Generating public/private rsa key pair.
Enter file in which to save the key (/home/willi/.ssh/id_rsa):
Enter passphrase (empty for no passphrase):
Enter same passphrase again:
Your identification has been saved in /home/willi/.ssh/id_rsa.
Your public key has been saved in /home/willi/.ssh/id_rsa.pub.
The key fingerprint is:
1d:cf:bc:0d:f4:c3:e6:d5:24:c5:ac:d9:38:5e:94:a8 [MD5] willi@server2
ssh-copy-id -i ~/.ssh/id_rsa.pub willi@server1
/usr/bin/ssh-copy-id: INFO: attempting to log in with the new key(s), to filter out any that are already installed
/usr/bin/ssh-copy-id: INFO: 1 key(s) remain to be installed – if you are prompted now it is to install the new keys
Password:

Number of key(s) added: 1

Now try logging into the machine, with: „ssh ‚willi@server1‘“
and check to make sure that only the key(s) you wanted were added.

willi@server2:~> ssh server1
Password:

Wo könnte ich nachschauen, was das Problem ist?

Danke und Grüße
Bozi

ssh -v 'willi@server1

Ausserdem solltest Du die Konfiguration des sshd von server1 mal ansehen. Stichworte wären:

PubkeyAuthentication,
RequiredAuthentication,

Nur mal so als Anfang.

Sebastian