Deciding whether to study abroad or continue at my current university for my PhD, what factors to consider?
One big advantage of changing schools is that you meet new people.  Most people have a few things they're really good at.  By meeting new people, you get to learn the new things that they are really good at.  More generally, you get to experience the culture of a different place and group of people (both academically and socially).  This helps to give you a more developed sense of what is normal (reasonable to expect), and likely will expose you to new insights.  All else being (close to) equal, I suggest that you move.