First, is requesting an H visa a disadvantage as an applicant? This is impossible to answer clearly. In general, an H is more expensive, more complicated, and more work for programs. J visas are cheap and easy. So, given that, you'd expect that programs would favor J applicants. However some programs use H visas to entice better quality applicants. My institution manages all of the visa issues for me, so it really doesn't matter. I have seen delays in start for both H and J visas. The fact that you're a US grad on an F visa makes an H much easier because of the OPT year. So, probably in general an H is a "disadvantage", but might actually be an advantage at some programs (that specifically favor H's) and in your case many programs may not care for a good quality US Grad.
Second, you ask what you need for a J, just in case. My understanding is that the MCCEE exam which used to be required for the Statement of Need is no longer needed. I would double check with your Province's Health Canada office. In that case, there is nothing you will need other than the application, proof of citizenship, proof of match in the US, and proof that the program you have matched to is ACGME certified.
