As an ex EU-grad-student that has moved to the US, one thing that really made a big difference for me was the opportunity to visit other schools abroad during grad-school. I strongly believe that this opportunity has been a major factor in both my development as a researcher as well as opened up career-possibilities I would not have had otherwise.
So long story short, I would see whether both schools facilitate spending time at another university if you hope to do so during grad-school.