i just came back on RTW with star aliance in D.(mxp/christchurch/wellington/auckland/nadi/lax/mxp) and had the worst experience only because I asked air new zealand to change a flight from wellington to auckland in the morning instead of the afternoon. After that I don't know why, they had to reissue the entire ticket and it took them 2 days as they couldn't get in touch with Lufthansa. ie we had to go back to their office at least 4 times and they said that they are not used to this kind of tickets.........The flights on Lufthansa were lost and when we received the new ticket it was all wrong with a different date for my companion. We decided to show up at the LAX airport anyway and it took them more than 1 hour to sort out all the mess as they couldn't even find my ticket number that air new zealand had reissued. Finally we were able to leave but it was a pain.
additional consideration: business class in Lufthansa sucks compared to Singapore and Air New Zealand. We asked to be upgraded to 1st using miles and more miles but were refused.....