Funnily enough, I have a friend who is also from the US planning to go into medieval studies (although he's doing his masters in Germany because it's a lot cheaper and they have some good medieval studies departments there - also I gather as for most ancient language areas, reading knowledge of German is indispensable anyway so developing his German language skills through living there was a convenient bonus). He also considered York but, because he really wants to continue in academia if he can, he feels that really only Oxford or Cambridge in the UK is likely to enable that. Unfortunately, medieval studies is a tiny field and so it's quite tough to stay in that area after the PhD.
Therefore, I get the impression one really does need to aim as "high" as possible for graduate studies in that area (unless she is interested in moving into a cognate area like archival work or early modern history or something). So, while York is very good and has a good medieval studies area (albeit, perhaps not as good as Oxford's), if she has offers from both I think it would be hard to justify not going to Oxford, unless it's completely financially unfeasible - at least for a PhD; at masters level it might be a little more flexible but I think she'd need to very carefully consider the offerings from both courses, especially language offerings (medieval studies PhDs almost inevitably will require working with the texts in the original language(s), unless it's a purely archaeological PhD project, so a good background in those is very important I gather).
That said, for Old Norse specifically I'm aware UCL has a lot of offerings in that area. Also out of Oxford and Cambridge I imagine ASNAC at Cambridge might be the stronger programme, especially for philological work. This of course is outside the scope of your question but if she also applied to either of those and you are awaiting decisions, that might influence things (alternately places to consider for PhDs).
Usually I don't advise chasing "prestige" or "league table rankings" but the above is based on what my friend of mine was advised by academics in the field, and he is definitely not one to consider such things without critical eye so I'm pretty confident it's not just spurious "prestige chasing" on his part!