https://mega.co.nz/#developers
Apparently, they use unsalted symmetric key encryption which allows them to discover [hash(file), password] duplicates. By comparison, the old Megaupload would apparently deduplicate based on [hash(file)] matches.
Suppose Alice and Bob have files [D, E, F] and [F, G, H], respectively. If MEGA discovers that Alice and Bob share a duplicate file F and Alice to reveals her password (through password frequency analysis or to the Government), then all of Bob's files are compromised.
I would personally feel unsafe storing private documents on Mega due to the lack of public/private key encryption, but that's me.