Stay put or enter the US application process I am an American who came to Europe last fall to do an MS which would complement my BA, since the field of study for my BA was different than my current one. My original plan was to apply to PhD programs in the US this fall, but recently I was offered a PhD position by my current adviser. I have until this summer to decide, which means I can either stay where I am now or decline the offer and cast the dice in the US application process.

In itself, my current department is not particularly well known in the US, where I would ultimately like to work. However, my field is small and my adviser is somewhat influential. Moreover, the advising is high quality. My adviser and I generally meet for one to three hours a week to discuss my work. I genuinely like my adviser, her insight, and the work I am doing. If I stay here I would also have connections to a lab in the US which is among the best in the world for my field. I would spend some time there as needed/desired, and the other members of my dissertation committee would likely be from this lab. 

There are several US departments where I originally planned to apply. They have good faculty, have a large number of students in the same subfield, are close to other institutions doing related research, etc. In short, if I were accepted to one of these schools, I might sleep sounder knowing that others have tread my path, and at least some have had a good outcome (solid reputation, decent job, etc.).

My situation can be problematized as follows. The offer from my adviser is obviously an opportunistic move on her part. As a friend of mine put it, “she sees a talented young scientist and wants to snatch him up before someone else does.” Regardless of whether the characterization is accurate, that's a way of looking at the situation. My task is to decide whether the move is the right one.

Has anyone had a similar experience or just care to share some insight?
While shane's argument has some merit, there is another important factor to take into consideration: time to degree, which is very much inequal here.

If you accept your professor's offer of a PhD position, you would in principle be able to start your PhD research as soon as this fall. If you were to decline the offer, you'd definitely have to wait a full year to start the PhD program, and then at least an extra semester or two, depending on the course requirements in your field. So there could be up to a two-year delay before you do substantial work in your PhD field, depending on whether or not the department will waive your master's coursework. This may or may not be enough to sway your decision.

Additionally, you should look at all of the "peripherals," including things like: 


how much teaching duty would be combined as part of the PhD position (this can be substantial, depending on your advisor's or department's teaching load!); 
what the benefits and support associated with the position are relative to the US programs you're considering; and 
what are the chances someone with your record will have to get into a comparable US program.