Rodrigo,
I've just filled my tran with Royal Purple Synchromax which is a fully synthetic oil specifically designed to replace ATF in manual gearboxes. It works fine (better than ATF on a cold day!) but costs a fortune!
My rear diff is now filled with Castrol SAF-XJ which is a synthetic gear oil specifically formulated for LSD type axles. I think this is the stuff BMW uses in the UK but you can only buy it in 25ltre drums which causes problems. Castrol Classic Oils can decant 5ltrs but again it costs a fortune!
Castrol's other suggestion for the diff was Hypoy LS. Check this link.
http://www.castrolclassicoils.co.uk/gear_oils.htm