I think they're both relevant today, but "I'm keen on..." is specific to British English. As an American, I don't think I've ever used the word keen in normal conversation. I would say "I like reading," or "I enjoy reading." I might say "I'm fond of..." in writing, because it sounds more formal to me. It's still acceptable and relevant, just not how I speak in informal conversation.
Likewise, my British friends often say they are keen to do something (e.g. I'm keen to see a movie this weekend), but as an American I would say, "I want to see a movie" or "I'd like to see a movie."