Definitely the second one, because my memory is that it's a book with a brief framing narrative about a modern boy called Kit, and then a long story about a bear-killing girl called Mox (who is apparently a boy?). I turned EVERYONE into girls as a kid... I was convinced Merry and Pippin were girls for years.

I liked a lot of David Almond's books as a kid, though. Was this your first?