I was in the midst of RTW issued by AA. Made changes to the itinerary, and tried to get Qantas to reissue.
1) In Wellington, QF ticketing couldn't even SEE any AA segments in their computer. Called AA New Zealand. She told me to have QF call AA and have the segments manually entered. QF would not do, so I had to call AA back and have HER call QF and manually enter the segments while I waited on hold for 20 minutes.
2) When I showed up at QF ticketing in SYD, they still could NOT see the AA segments, so were unable (unwilling) to ticket. Plus, I was at airport with 4-hour connection, and was told that QF ticketing was too busy to do any same day reissues.
3) Upon arrival in LAX, tried to get AA to reissue the ticket. She had to call tariff and have the ticket re-calculated. She was unable to finish, but I was going to JFK and she told me that ticket would be ready for quick issue in NYC upon my arrival. (Ticket agent came to departure gate to tell me this). In JFK, ticket was NOT set up for ticketing. Woman had to again call Tariff and it took 20+ minutes but she was able to finally reticket.
Conclusion: Always better to have reissues done by AA ticket agent when you are at home and have adequate time. I guess I should have known.

The various Oneworld systems are incompatible and they really cannot see your PNR info unless it is explicitly pushed from one computer system to another. Certain transactions cause an attempt at an automatic push (usually this results in each system having a different subset of the info). When an agent runs into this on a reissue you will have tremendous problems unless they are very skilled and persistent (usually they must over-ride several different things in ways that are not usual). Be glad you didn't try to reissue with BA who would have charged a 25 GBP fee on top of the 75 USD reissue charge (and made sure you got many hours of "entertainment" for that 25 pounds).
With the move to e-ticketing across OW airlines I am curious to see how these kind of problems are resolved; I'm holding an e-ticket with flights on CX, AA, BA and have had no problems so far, but imagine when the agent says: "I'm sorry sir, there is no reservation in our computer for you". And there is no paper to prove otherwise (the PNR printout is easily forged so they can't possibly accept that as proof).

As others have said, it's all who you get. I recently had one done by CX in Hong Kong in about an hour and a half. Most of that was probably because I left to go eat lunch or I am sure it could have been sooner. I have had AA take literally days and still screw everything up to the point that I took the ticket to BA. In all fairness, though, AA has done quick ones for me as well. The Wellington thing, frankly, sounds like incompetence and laziness to me. There is no reason they would have needed to see the AA flights. Build the damn ticket, leave it as open, and just go off the original PNR for the reservations.

The last DONE4 I had re-issued (added two new segments and changed dates of remaining 3 segments) was by BA at LHR T4 and took no more than 10 mins and no charge. I was surprised as I handed over the credit card and was told there was no charge. But this was about 2 years ago.

Its always better to have the issuing airline to the re-issue if you possibly can. Not always possible when you are part way through a journey.