You need to contact the education board in the countries you're interested in practicing in. Back in the day, although I hope to ultimately get an H1B sponsored and stay , I wanted to make sure that my degree is useful in my home country. I asked specifically about PhDs in Clinical Psychology (so not PsyDs), and was informed that it needs to be from an APA accredited program. In addition, because at the time I wasn't sure whether I wanted to go for a research-only PhD, I also inquired about that (since there is equivalent accrediting body) and was told that it would be considerably easier if the degree came from a reputable (think R1) university. I was also told that I would always have to list the actual degree - so, even if you're allowed to perform certain jobs because your degree has been deemed equivalent to those common in your country, you would not be allowed to state that you actually hold that country's degree. Because the PsyD is not really known outside of the US, I can image that this may cause some issues. US degrees also tend to be looked down upon (rightfully so at least for undergraduate degrees, but that's another story)
Another thing is licensure. Just because your degree has been deemed equivalent to another degree, it does not mean that you have automatically met the requirements for licensure in this country and may be need to complete additional training, courses, etc.
All of this is information that I obtained several years ago and not for one of the countries that you're interested in, but I hope it helps at least somewhat.
