The BBC website has an article on nosebleeds here:
http://news.bbc.co.uk/1/hi/health/262462.stm
The causes here include dryness, altitude and allergies amongst others.
I would say that on the 777 I feel very dry after a long flight and drinking a lot doesn't seem to help. Altitude is unlikely to be a factor as this is usually at very high altitudes when climbing for instance. Allergies could be a factor, I have no idea what the filtration system is on the 777, but if it was conducive to mould growth then there is an outside chance, but I doubt it.
Certainly the 777 is a dry aircraft from a pax point of view and I would suggest this is the main reason.