The fellowship game is pretty much like the residency game, and just like the residency game it varies with the amount of competition.
The more the competition, the more your: visa status, place where you graduated, USMLE scores, lack of research/publications, inservice exams, certification board scores etc etc will be scrutinized to filter you.
Someone posted an article somehwere here on SDN showing the difference between what residency program director thought fellowship program directors cared for and what fellowship program directors actually cared for. I think the fellowship compare cardiology vs. GI/Nephrology?
If I remember correctly, it turned out the number 1 and 2 factors were you your performance in residency in the residency program director letter and the program director calling on your behalf.