I realize there are several threads about how important a brand name university degree is, but I haven't found any very applicable to my situation because:
1) I'm talking about PhD programs
2) I'm comparing programs in different fields
My story is this: I'm from the Netherlands, where I graduated from a bachelor's in Artificial Intelligence and a master's in Cognitive Neuroscience. (the quality/name difference between the universities are not nearly as big as in many countries, so it doesn't really matter which one it was exactly). Currently I work at a very prestigious university in California as a research assistant.
My consideration is this: I've been offered a PhD position in robotics at a relatively young university in Germany. From what I can tell, the group is not too bad but not extremely good or well-known either. The past years I've discovered that I'm really more interested in tech, so a PhD in CS is more attractive to me. Given my background and experience I doubt I can get into a prestigious AI/CS program in the US, but I think I have good chances in getting into a good Neuroscience program (but I can't be sure of course). In case of Neuroscience I would go for projects in Computational Neuroscience. Through my current job I have witnessed what a huge difference it makes to be at a big-name university, where large companies actually come to find hires. The whole area is also geared towards tech and innovation, so it's a great place to talk with people who have experience and are willing to share it.
Imagine I would want to work at Google or Microsoft, or start up my own company in the future, what would give me the best chances of success? I think I will have more relevant skills if I take the PhD in Germany, but there are all aforementioned factors to consider too. Another option would be to apply for other CS PhD's in Europe, but I wouldn't know which "well-known" universities would give you the same edge as here.
On one hand I love living in California and I'm afraid that if I take the spot in Germany, I won't be able to get my foot in the door here if I want to come back later. On the other hand the project is interesting (mainly machine learning), and I would prefer it over neuroscience projects.
I realize it depends on what kind of projects I can finish during the PhD, but let's say it's not going to be bad and not genius either.