From my standpoint (Brown med student: have done my core rotation and a sub-i in medicine there), it's a good program, but I suppose I haven't got a lot to compare it to. Most of the residents are pretty bright, and they seem to be well trained by the time they are done. There is generally good morale amongst the housestaff, in large part because the program directors are known for having their resident's back, and also because of very non-hierarchical relationships w/ attendings, and I think this helps to attract a crowd of residents that are balanced and have interests outside of medicine. Fellowship placements are generally very good; I haven't heard of anybody not getting what they want in the time I've been here. Especially strong departments include Heme-Onc, Pulm/CC, ID, and primary care, so a good number of residents go into these fields, but there are people heading into nearly everything, including cards, GI, etc. and they get good spots too. There is a lot of global health work going on here, so there's a visible subset of residents who come here for that reason.
The program is not just at RIH. RIH is the large, urban, academic center where most of the rotations take place, but residents also rotate through the Providence VA, as well as the Miriam hospital, a nice community hospital with a wealthier (and sicker) population, that is actually very well regarded locally. Each site has its own quirks, but all are generally considered to be educationally strong by the residents.
As for competitiveness, it's hard for me to say, as I don't usually ask the residents I work with what they got on their boards, or if they made AOA
My sense is that it's definitely on the more competitive side of things, but it's not in the MGH/BWH/Hopkins/Columbia/UCSF/etc. tier. My guess is that it's similarly competitive to places like BU, NYU, and Einstein/Montefiore. If your school has sent people to Brown's IM program before, they can probably give you an idea of what your chances would be of getting a match here.
Hope this helps. Let me know if you were looking for something more specific.