I share Matthew's opinion. Qantas is really excellent - booking was very quick, follow up as simple as it gets and even a tax reimbursement has gone without a hitch (and I didn't have to send anything).
The team at the FF desk is also pretty friendly - had a long chat with one of the girls there about Concorde, she then made sure that all seats requests were processed and even called back.
AA is actually also pretty good - a little tip - if you can’t process a booking via the web, call the reservation line but instead of talking to the sales team, ask to speak to the internet support desk. They can process any booking and are really efficient.
Having said that BA, in my experience, tends to be good – friendly staff and quick bookings over the phone. It’s when something goes wrong or is out of the (very) ordinary that things start to get worse from a Customer Service perspective (unless you’re Premier or a Special Services’ favourite, etc... yawn).