im a DO student, so obviously im biased, but i have done a lot of rotations where there have been carribbean/foreign students and i have hung out with a lot of them. being a carribbean student makes your 3rd and 4th year so much harder- there are a million more hoops to jump through as far as approval, etc. goes for rotating in the states. i just remember they were always having problems with rotations, and they were always calling their schools, and faxing things around. i dunno. it always seemed like there was more paperwork and protocol and crap to deal with. and different states required different things from them, and every hospital required different stuff. if you're a DO, you dont run into any of that, because you are an american student, and your school has affiliates, and rotating at elective sites doesn't require anything different than what an american MD student would have to do (although i will make a disclaimer that i know nothing about ross specifically). as far as landing an actual psychiatry residency spot, i dont think DO vs IMG makes a big difference. i interviewed at mid tier allopathic programs, and they all had at least one or two DOs and/or one or two IMGs in each class.
but i agree with the above poster who pointed out that your name is MD Driven (and not DO Driven) ... if that sort of thing is important to you (which is fine), you will not fit in at a DO school, trust me. most of us have got a lot of pride and most of us can tell who really wants to be a DO and is super into it, who doesn't really care either way and is happy with being DO, and he who would really prefer to be at an MD school and is generally bitter and disastisfied with life.
dont let landing a residency spot be your determinate- if you are smart, nice, and you rotate at places you are interested in applying for residency, you will probably end up where you want to be regardless of where you went to school. so if you're MD driven, then go carib or foreign or whatever. but i def think DO is an easier route in the long run. plus you'll be able to crack people's necks.