What are the long-term advantages of a US PhD compared to Europe/Oceania?
I think the key question is: What do you want to do after the PhD?

There are some points that you may consider to choose a programme if you want to stay in the academia. The advantages or disadvantages of the length of these programmes depend on your training/background.


Your background. If you are familiar with the topic you are planning to work on, then you can probably start checking the relevant literature immediatly, in this case a 3 years program may be what you need. But if the topic is unfamiliar to you, then you would probably have to attend lectures and to read textbooks, in this case a 5 years program may be better.
Your CV. A work in the academia usually involves teaching and research. If you have teaching experience, then you can focus on developing your CV in terms of research. In this case I would go for a 3 years programme and get involved full-time on research. If you do not have teaching experience, then you might want to consider a 5 years PhD where you have the opportunity to teach and develop your CV in both lines.
The topic. Some research projects by their nature itself require different amounts of time to develop. For instance if you are going to work on modelling a specific data set vs. having to obtain the samples directly in the Amazon.


Regarding the mobility, I think after the PhD what really matters is your CV. Either if you graduate from Oxford or the University of Tuvalu.