I went to OHSU for med school and have a modest amount of insight having done some rotations though these systems, although I did not interview at any of them for residency. No doubt some would disagree, but IIRC the general consensus is that Providence Portland is the best community IM program in town, followed by Providence St. Vincent's, distantly followed by the Legacy Emanuel and Legacy Good Sam programs. The Providence hospitals are legit tertiary centers with high volume and complicated referrals. I think the relative competitiveness is in keeping with this. For whatever it's worth and whatever it means to you, I don't recall there being many (any?) FMGs in the Providence system, but many FMGs at Legacy.
The other non-university residency option in Portland is the Providence Milwaukie family medicine residency, if location is a must and FM is conceivable for you. I think it's a relatively new program, and I imagine it would not be particularly competitive.