I have flown the 777 for 8 years now and actually operated one of the 'air quality' trials done about 6 years ago.
The techies conducting the trials were close lipped but I did manage to notice that the relative humidity in the flight deck was 4%, the cabin was a bit better as they get less fresh air.
I dont suffer from nose bleeds but do get very dry eyes. I do my best to lubricate with drops, although one has to be careful as many types of drops carry a warning about blurred vision. ( An improvement to my flying some would say!).
The other reason the 777 generates problems is its relatively rapid climb. On a 747-400 long range sector the first few hours will usually be spent at an FL in the low 30s, giving pax/crew time to acclimatise a bit before the cabin alt gets all the way up to 8000'.
The 777 often goes straight to the high 30s or even FL430, pushing the cabin alt to 8000' immediately.