I just happened to come across this issue writing a final exam for a course in international financial derivatives regulation. (For those of you who don't know what that is, it's what you do in purgatory.) Both spellings are correct. In general,"adviser" is the preferred spelling, especially in the UK. "Advisor" carries a connotation of someone whose professional capacity is to give advice. On that basis, and since my course had a strong focus on American regulation, I changed "adviser" to "advisor" regarding "very-high-net-worth individuals ... who tend to employ the service of sophisticated advisors to assess and manage their risk." If you want to know my sources, just google "adviser or advisor" like I did and you'll get them all.
Can't resist taking a swipe at the obiter on "amount" vs. "number" in the media. My two fields are English Literature and Law. Like Law, English grammar is based on rules which must be faithfully applied in order to preserve a unified fabric, but like Law, English is (forsooth) a living language. It lives and is preserved our media of communication. When the editors of the OED want to know what the "correct" usage of a certain term was in the 19th century, they turn to ... the media! I'm the first to be a stickler for good usage, but don't overdo it.