PhD. in the US directly after European BSc., or is it better to go for a MSc. at first? I'm currently in the final year of my BSc. in physics and the second year of my BSc. in mathematics at a university in german-speaking Europe. I'll have my degrees finished in summer 2018.
Eventually, I'd like to end up in theoretical or mathematical physics research (most probably gravitational physics) and would love to experience some time at a foreign university. Firstly, since my university is stronger in the experimental field and has a relatively small theory group and secondly for the sake of broadening my horizon. The US (or generally Northern America) would be particularly interesting, because of the somewhat &quot;more open&quot; research culture, in comparison to a highly bureaucratic and kind of inert (and often poorly financed) apparatus in german-speaking part of Europe (and probably in the whole EU - at least that's my naive perception of it, or am I wrong in this?).
I read that the PhD. in the US is a bit different to the one in Europe, e.g.  that a MSc. is kind of integrated in the coursework-heavy first one or two years of a US PhD. Nevertheless, there are some interesting MSc. programs in Europe, e.g. in Edinburgh or at the ETH in Zurich.
So, my questions would be (from a rational/scientific-career point of view):

Is it reasonable to go for a PhD. directly after a BSc. in the US? Or would it be more sensible to pursue a MSc. in Europe first and only then head for a PhD. in the US?
Small side question for physicists since I'm just researching into this: Which universities in Northern America have a strong gravitational physics department (aside from Stanford and Princeton)?
In my opinion,

there will be many challenges in deciding to move to US.

First of all you will have to adapt to a society that despite having a western culture, is still very different from Europe. If you are not able to adjust culturally, it is highly possible that this will affect the progress of your studies. Cultural shock is something most international students experience and usually takes a semester or a year for its effects to wear off... However some people have more difficulty adapting to specific cultures from what I've observed.

Secondly there are many structural differences in US and European PhDs. For example, you will have to earn a Master's degree by attending classes while you do your PhD in US. At the same time though most professors will pressure you to make progress with research, which makes things really tough. Keep in mind that in order to maintain your visa status in most universities you will have to maintain a relatively high GPA. On the other hand you will also have to please your advisor with your research progress or he/she may convert you to Master's status, and you will loose the opportunity to earn a PhD.

The rationale behind taking classes, is that Americans want to guarantee that their graduate students have a certain amount of exposure on advanced scientific topics. Whether this is a better practice or not compared to the European programs that give much more emphasis on research, I believe is a matter of personal taste and preferences.

What is more if you earn a Masters from Europe and then move to US for a PhD, it is highly likely that not all the classes you had, will be transfered to the new program. You will also be older while you enter a commitment that may last many years. Some may argue that you will be more experienced to face the challanges that come. However I think that the younger you finish your PhD, the better...

Also keep in mind the following general things (some of which also apply for European PhD programs):


PhDs in US take longer to complete (Europe = 3-5 years, USA = 4-6 or
more years)
Before joining a lab make sure you can collaborate with the professor
that leads it. If you feel that you can not collaborate leave and
search for other opportunities that interest you. Although many departments allow grad students to change labs after joining the program, it may not be an easy process due to starting over with a new topic as well as politics between different labs.
Additionally, ask in a polite way the professor running the lab or other lab members what are the requirements to graduate from the lab (e.g number and types of published papers). If you don't get specific answers be careful before joining.
If you pay a visit to a lab for an interview make sure the testing
period lasts for at least two weeks and try to find out how other members of the lab feel about what they do. If the majority does not 
seem satisfied leave and search for something else (pay attention to
people who exaggerate though...)
Depending on your field there might be more job and money related
opportunities in the US, but I believe the whole experience will be
more tough and you will have to decide whether this thing contributes
to your career or not, from early in order to not regret spending
5 years on something you did not like.
There is a high dropout rate in American PhDs. However, I think
that the fact that you will have international experience might make you
seem more valuable in the eyes of potential employers in the future, if you manage to complete the program.