Bjork for me. I can see her being a kind of hair-pulling, groin-kicking (and maybe she even knows some kind of martial art?) brute force type of fighter, while Joanna Newsom is probably too fey to put up much of a battle against the older, sterner Icelander. (They live in the freezing cold with barely any sunlight you know! Tough as nails!)
But on the other hand, Joanna is young and (probably relatively more) nimble. Plus she's experienced with delicate handiwork. Should she have a pack of those nylon harp strings to hand, she could be stringing up and choking Bjork, before one of her overwrought IDM beats has the chance to properly kick in. Bjork will have to take advantage of that space where Joanna recites some over-long victory prose to reclaim some advantage over the American.
In summary, Newsom has only an outsider's chance here. Bjork used to be a punk, and will surely be able to recall and utilise those trusted skull-cracking skills by sticking the boot into a prim, old world Rapunzel like Newsom.
What say you?