the dialogue is the same as that of the Secret Ending from the previous game:
http://www.youtube.com/watch?v=h-OcCm_HiZY
For convenience's sake, here's the official English translation as well:
http://www.youtube.com/watch?v=ZHUfbWDE1BM
The text part of the Report also says that this takes place at Order's Sanctuary, so while they've changed the scenery for the conversation, it apparently takes place where it always did.
Anyway, almost the entire conversation is the same, with the exception that there's a few extra lines in which Cosmos demonstrates that her balls have finally dropped. I think I have a pretty good handle on what was said if anyone's interested.
After Cid says "We shall journey on the road that continues to the final fantasy..." Cosmos says "No. I will remain here. We cannot know when this world where balance was lost will sink into the Interdimensional Rift."
Cid asks her if this is the path she has chosen and she says yes. I'm not positive, but I think he apologizes for what the "endless cycle of battles has done here."
She says there's no need, and that rebuilding the world is her undertaking. She then asks Cid to walk her path as well, bids him farewell, thinks of her victorious warriors, smiles, and walks off.
I'm not too sure why the developers chose to revisit this scene in this manner, but my guess is that it was to quell all the notions among fans that there could be another cycle after the last one ended. We do still hear people saying that the Secret Ending of the first game implied that there would be a 014 (despite all evidence to the contrary), so Cosmos telling Cid to go fuck himself (that's not quite what she did, of course, but she does go off to do her own thing) should soundly put that to rest.