If the school is AVMA accredited, then you can practice in the US afterwards, provided you pass NAVLE and boards for the state you want to work in, with no additional steps. Your education and degree will be considered equivalent to a DVM earned at a US school.
Accredited schools in the Carribean are SGU and Ross. Australia and New Zealand has Massey, Queensland, Murdoch, and Sydney. In Europe, there's Edinburgh, Glasgow, RVC in London, and UCD. I believe that I remember also seeing somewhere that there are now schools in the Netherlands and France that are accredited, too. Mexico has UNAM, and I believe virtually all of the Canadian schools are also accredited.
Here is the complete list:
Members
Otherwise, if you attend a non-accredited school, you can eventually still practice in the US afterward, but there are more hoops to jump through. You'd have to take an equivalency exam, either the ECVFG or PAVE. The former of which is the more expensive and (reportedly) far more difficult of the two, but it will allow you to practice in all 50 states if you can pass it. It also contains a Clinical Proficency Exam with an absolutely atrocious failure rate. PAVE is only accepted in... I want to say 30 states...? Feel free to correct me on that. You will obviously still need to get through NAVLE and state boards, as well.
The ECVFG and PAVE are both very expensive exams to take, especially the ECVFG, and many doctors have to sit them several times to pass. I would just aim for accredited international schools to avoid having to go through that process, if at all possible.
I applied to Glasgow last year and was not accepted immediately, though I was off of the waitlist, despite having already been admitted to a US vet school. So I personally wouldn't say it's significantly easier to get into an international school than a US school. Perhaps in the past, that may have been true, but I'd say that the admissions processes are probably just about on parity now with the increased competition/numbers of applicants.