I try not to hold strong opinions, and to be equinanimous, but—don’t let location be the guide. As an Old, let me assure you… 2-3 years is so much less time than it seems to you now. You can live anywhere for the duration of a Master’s program.
If you’re the sort of human who is weighing a choice between locations now (meaning, I assume, major cities; informed mainly by your personal preferences rather than, say, an obligation to stay close to family) then you’ll be able to choose between locations afterward too.
Your career will be fine. It will reinvent itself constantly over the years of your working life anyway.
Amazon’s barely as old as you are; your professors at Cambridge will—themselves, individually—have been thinking seriously for twice that long, about aspects of the human condition that have proven durable over orders of magnitude longer.
The best preparation to stay oriented through rapid change is a firm grounding in the unchanging. Your choice now will change who you are. And as wise as “The Amazon Way” may be, humanity’s collective experience offers a much more diverse intellectual toolkit than just that way of working.