system
Given the following post, respond as if you're commenting on Reddit:
human
How much of an impact does it make to complete your PhD in the US versus Europe/Oceania/etc?

I have read a few times here that US institutions prefer people who hold PhDs from the US in hiring, and I'm not sure if a similar idea holds for other countries/areas. I'm not sure if it'd be more difficult to be accepted to a grad program as an international student or a post-doc position as an international early-career researcher. Whilst I'll probably spend at least part of my career in the US due to how many research groups are there, I don't intend to live there permanently if I have an equal choice elsewhere. I may change my mind on that in the future.

After completing my undergrad + honours in Australia (in Physics, focussing on Astrophysics), I am also concerned that the "method of delivery" for the US PhD won't suit me. I'm already used to being pretty independent in research and am not looking to sit in heaps of courses anymore or do rotations; I'd prefer to identify a project and start research on day 1, if not earlier. So on that front alone, it seems like the PhD style for Australia + Europe (and maybe elsewhere) would suit me better, but I'm aware that there are other benefits for drawing it out over longer and getting more teaching experience. 

**Is there any, even incredibly slight, advantage in the long term to taking either path in terms of an academic career?** There are places (and academics/groups) that I want to apply to all over the world, but the GRE requirement and processing fees for most US institutions are expensive, and I need to cut down the pool of places to apply to. Of course, I'm skimming over details for visas, funding, maybe language barriers, and even getting accepted to begin with, but those will largely have to be taken into account on a case-by-case basis.
gpt
Go to a school with a department that focuses on something you're passionate about that has funding and faculty interested in the same thing.  Write interesting and relevant papers published in credible journals.  Network and meet people in your field and collaborate with the best and most active people you can find.   The US vs Europe thing is small potatoes vs this stuff.  Chances are if you are relevant, you'll know people in Europe while working in the States, or visa versa, and those will be the contacts that hire you after you graduate.  If Dr. Awesomesauce at Cal Tech likes your work, he'll hire you no matter where you go.  So go where you can do the best work.