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.
I think PhD programs differ in three main aspects: duration, teaching, and coursework. I would prefer not to try and generalize how these aspects vary amongst different countries. That said I think a PhD program with limited coursework and teaching are beneficial, especially if you already have an MS. Some teaching might be useful if your personality is such that at job interviews there would be questions about your ability to engage students. Picking up teaching experience is relatively easy and I would not consider the ability to gain teaching experience as positive in deciding on a PhD program. Similarly for coursework; the ability to take courses is not a positive.
Duration on the other hand is a big factor. The longer the duration the better. As hard as it is to be a PhD student, it only gets harder. Putting off becoming a postdoc, and then again the tenure track, for as long as possible is a good thing for your research output and will help you eventually get tenure.