Now that I have been a part of academia in both North American and European settings, I have slowly seen differences when it comes to how one studies and gets a terminal degree. I don't really mean to write a how-to type of article here, I just want to pen down some observations I had made, and so take it for what it's worth.
See, when I decided I wanted to go to graduate school, it never even occurred to me to look for programs that might interest me in Europe. Primarily the reason for this was language; I only speak English, Filipino, and Japanese fluently and professionally (in 2003-04), so I mostly concentrated on finding programs in the United States. And given my (personal) field of interest, there was one particular school that really made sense (at that time), so I only applied there and fortunately, I got accepted.
Later on, I wondered what would it be like if I did things a little different.
Anyway, it seems that if you want to get a PhD in a European setting, chances are you need to find an open project. What this means is that there is a professor who has a grant and is looking for a student to fund, because this student's research will address some of the research questions that the grant touches. In North America, on the other hand, things are more fluid. I have met students who eventually finished graduate school who when they began the program, they didn't have a specific project in mind, just that they wanted to study the field.
So one big difference here is that of specificity, and the freedom (or lack of it) that comes with it. Do you already know what you want to do? Have you found a project that will fund what you want to do? European programs, in my opinion, are less fluid and constrain the student more. What if there is no research fund that directly coincides with your interests? I can see a scenario where a student applies to a project, not because he really is interested in this project, but only because this is the project that has the most overlap with his interests. In short, I have this observation that the European model gives the student less freedom to flourish and develop. If a student has no idea yet what sub-field one wants to study further, then I think the North American model is better. At least in my personal case, the North American model has been an advantage to me.
Speaking of which, the North American model has plenty of coursework. Or classes. In graduate school, I had to take 72 credit hours (or 24 classes). 30 credit hours were for the masters (MA) phase, while the remaining 42 were for the PhD phase. That meant that I had to attend classes and perform well on these classes while doing research for my dissertation. And sure enough, sometimes you don't have plenty of time. So dissertation research gets the backseat at times, which means that once you finish those 72 credit hours, you still have to be a student, and maintain enrollment, in order to do dissertation research. European programs on the other hand, do not require students to attend coursework, in the PhD phase, at least. If I understand the system correctly, in Europe, one does a MA degree first, and then one lands into a PhD program only if one has an MA degree. The PhD program is a 3-year research-only program. In North America, one can begin a PhD program without a MA degree (I didn't have one when I started), and the combined MA-PhD program lasts between 5-7 years on average, with shorter times in the natural sciences and longer times (say 10 years maximum) for the humanities.
Now this might seem like the European model is faster, yet more restrained. It's all up to everyone to decide what works for them. What I like about the North American model, however, is the fact that one emerges from the program more well-rounded. I certainly met people who did the European model and know things only about their research, and knows nothing about the other sub-fields of their field, simply because they weren't forced to take courses about them.
Obviously, there are good and not-so-good things to both models. I still prefer the North American model (if I were to repeat my PhD experience, which I won't, I would still select a school in North America), but obviously, the Europeans have their system working for them as well.