Both are top notch programs in NYC. You probably already know the answer because you have highlighted some of the major differences between the two.
Jacobi definitely has the edge in patient diversity. Both can be accused of too much of the same...poor, underserved communities in a "county setting". However, Jacobi's encachment area includes many diverse neighborhoods. On any given day you can treat Hispanics, Albanians, African Americans and Asians in all shapes and forms and in all three different classes. Whereas, Kings County serves primarily African, West Indian, and Carribean populations with a slither or Eastern Europeans. As you can imagine this mix is a hotbed for cultural adversity...hence lots of gangfights, and need for "respect in the street".
True, the majority of trauma at Kings County is penetrating. Kings county is the true knife and gun club of NY. While Jacobi continues to receive its own share of the knife and fun club, you will see more of it at Kings County. Jacobi is central to many intersecting highways, primarily I-95 connecting Boston to NY. Some of your patients will include soccer moms racing in their BMW SUV's who roll over on the highway. The son of a MAJOR CEO (with a company named after him) rolled into the ED unconscious. His identity was only discovered because he happened to be "(title company) Jr." on his driver's license. He confirmed this after he regained consciousness. The patient diversity tends to "liven up the day" with some interesting conversations to break up the routine.
Regarding reputation and "academics". I really cannot comment, sorry. I can say that the chair of emergency medicine (Dr. John Gallagher) at Montefiore is a major force in Academic Emergency Medicine and is one of the editors of Annals. He has written a ton of articles and is well respected in the field. He is integral to the Jacobi/Monte program, and is often seen in the ED thouroughly reviewing cases with Sub-I's and residents.
However one of the major strengths of the program at Kings County is the integration with the MPH. If you advise the director upon entering the program it can be arranged for you to finish the residency on time along with earning the MPH from Downstate.
When it comes down to it....it's always a matter of where you want to live and how you think the training will benefit you in the future. Either program will make you a clinical star! Each has incredible volume, acuity and pathology. As I alluded to before, Kings County is truly the knife and gun club...would you want to live in the area? Not if you want to roll into work on a stretcher shot by a "stray". So if you do, you look towards a little commute for piece of mind. On the other hand, Jacobi is oddly enough on a tree lined street in a pretty decent neighborhood. Don't get me wrong, there are some neighborhoods that are definitely a no-no in the Bronx, but Jacobi is situated in a middle class neighborhood. Also, Montefiore offers housing at a very economical price compared to NYC housing rates. Rents for a 1 BR are less than $700. While this may seem high for the rest of the country, $700 in NYC is considered decent rent for a parking space!
Good luck on your decision!