It appears that all NPCs that were using the old eagle model were updated to the new one at some stage during Legion. I'm pretty sure it wasn't at launch because I checked a few times around that period. Perhaps it was in 7.1.5. Minipets seem to have been updated too and I notified Quintessence.
Hopefully the change won't upset anyone with an older bird, because it's comparitively subtle. If you compare the old and new you'll see the colours are a little different on some (notably the white is more shaded and less bright), but all in all I think it's a really nice update that keeps the style of the original while increasing the texture.
I've updated Petopia to reflect this change. Please let me know if you find an NPC still using the old model.
One glitch: Zedxrgal noted that the Silkfeather Hawk, which was the only old model hawk to come in two colours, now only comes in white. It seems they forgot to add the second colour (light brown/white) back. I'll let them know.
