Transmisssion oil and milles/km with it

Hello everybody. I'm thinking to change final drive oil, and I've reading people who uses Honda specific oil (at the manual in Europe 10W40, same as at the engine) and other people who uses specific oil transmission 80W90 or similar. I think all 2 options are right cause our final drive conditions are not like a gearbox car or normal bike, but I´m not sure and would be more information. Can anybody write me wich oil use and milles with it?.
Thanks to all.

The documents attached are taken from the owners/maintenance manual for our 2005 models.

Thanks Dale.
In a European manual 2006 only says engine oil 10W40 SE,SF,SG. Any different oil experience?.