Both York and Nottingham are centres of excellence for Medieval Studies, so I can see why it's a difficult decision to make.
-Check out the research interests of departmental staff. If you know what you will write your dissertation on, who could supervise you?
-Taught modules - which institution offers the most interesting and useful mix of courses? How much emphasis do you want on development of linguistic or technical skills (e.g. palaeography)?
-Which institution offers the best hope of funding?
Hope this is of some help, and congratulations on the offers!