As for quitting a fully funded PhD program in Gemany to come here, you really need to look at the financial side of things. Tuition wavers are not overly common in Canada, and most Canadian universities charge international students a higher rate than domestic students. From what I have seen, the tuition can be upwards of $15 000 a year. A typical PhD stipend here would be around 19-20 000, which dosnt leave much to live on.
I'm not sure where you are, kron3007, but I've been a director of grad studies at a Canadian research university very recently, and we certainly do provide tuition waivers of various sorts. My university reduces tuition for international graduate students to the domestic level as a matter of routine, and in addition provides many funding packages that waive tuition entirely. In my own humanities department, a typical package would be a tuition waiver and a stipend in the low 20s for the first year, with no teaching; the amount of total compensation increases in subsequent years with the addition of teaching assistantships.
It is true that international students cannot compete for Canadian federal funding (from SSHRC, NSERC, and CIHR) until/ unless they are permanent residents; however, research institutions will often calibrate their support packages for top international recruits to the levels of support offered by the federal granting councils.
Your best bet, OP, is to consult the web pages of the Canadian universities in which you are interested. You will certainly find information directed specifically at international applicants, outlining the possible sources of financial support.
I have been a grad student in 2 Canadian universities in a STEM field. The first did not cover the difference (although there may have been some competitive scholarships available) and this was a major problem for some of the international grad students in my department. Even as a domestic student, I recieved a stipend of about 18000, tuition was about 6000, leaving 12000 to live on. We could TA on top of this, but in our department the positions were very competitive and there was no assurance you would get one. The second school I attended provided me, and I believe international students, with full tuition wavers. I was given the impression that there are only a couple universities in Canada that do this although I know many do cover the difference.
I guess the main point here is that you can not assume that your tuition will be covered in Canada, and it is prudent to research this sooner rather than later unless money is not a major issue. Like I said, I have met international students that were in pretty tough situations because they didnt research this fully before coming to Canada.