Ambition difference between PhD student and the supervisor

How harmful is it for a PhD student to work with a supervisor whose ambition is greater or lesser than that of the student?

I can imagine that if the supervisor aims much higher than the PhD student the experience could be nightmarish for the student (and frustrating for the supervisor). Similarly if the supervisor aims too low (something like: "Just generalize this theory in way X, that should be enough for a PhD") the work could feel meaningless and the time spent on it wasted, when more challenging and maybe even more important questions could deserve the attention and resources.