I can't speak for Columbia but, as a current resident, I can say the residency program at Mount Sinai is very, very strong and continues to grow every year. The fine print: I'm biased but I believe I have good reason to be.
A few points:
-As previously mentioned, IR is very strong. While ~2 of 4 stay for fellowship, typically others choose to go elsewhere to get a more diversified experience. Residents who are interested in IR do many of the procedures that fellows perform, including radial artery chemoembolizations, UFE's, percutaneous nephrostomies, ablations, etc., in addition to usual set of lines, ports, and drainages. The attendings have strong connections to IR programs across the country. Out of the 5 people who applied to IR from Sinai last year, 2 are staying at Sinai and the others are going to Stanford, USC and UCLA - all top notch programs. The current head of IR who took over when the last one left is very, very well-known in IR (as are all of the attendings at Sinai) and the program continues to get even stronger.
-IR is not the only strong division at Sinai. Neuro is very well known at Sinai and body is quickly becoming one of the strongest programs in the country. The latter is partially due to the body MRI program. Sinai now does almost as many body MRI's as CT's, which is probably how many places will look in about 10 years. There are 9 clinical (not research) MRI's (there are several more research magnets) and the caseload includes liver (Sinai is a very busy transplant center), prostate (the new head of GU has the busiest prostate CA practice in NY), MR enterography (Sinai has one of the busiest IBD centers in the country - Crohn himself was at Sinai), and more. Residents interested in MSK have gotten top-notch fellowships (e.g., HSS, Beth Israel in Boston, UCSD, etc.) and section, while small, is very, very good.
-Historically, Sinai had less research emphasis but some divisions are research powerhouses now. There are Sinai residents now at every major IR conference with presentations/posters and Sinai residents have published original research in JVIR, CVIR, AJR, JACR, etc. The head of body MRI is one of the most well-known researchers in the field and several residents and fellows have worked with him and his Ph.D.-filled lab on projects. Residents have also published with body attendings on projects in ultrasound and CT. In neuro, residents have attended and published in AJNR and written textbook chapters. Also, I've heard our MSK attendings are kickstarting a research program. All of the national buzz on CNN, NBC, Fox News about low-dose chest CT screening? All out of Sinai. Nearly half the residency attends RSNA every year with projects. Several senior residents are PI's running project teams filled with residents, med students, etc.
-Nighthawk did take away from CT volume for awhile but 2 major overhauls have changed/will likely change that (1 has been implemented, the other will likely be implemented shortly). The first is the creation of a 3-11 pm shift for senior residents - I'd guess that about 60-75% of the CT volume is during these hours and residents have no shortage of CT's to read with this shift. While a body attending is present, peds, MSK and vascular CT's are read by the resident with no attending read until the morning. You will be forced to make a call and feel very comfortable taking responsibility for a radiology department. The second change is with regard to Nighthawk - there are rumors that the new ER radiology section will be taking over all night work and this will likely lead to a very positive resident experience. By the way, Sinai is one of the few places with no ultrasound tech on overnight despite a busy service and Sinai residents feel very comfortable performing ultrasounds (all 1st trimester ultrasounds, for instance, are handled by radiology).
Both are likely strong programs and you likely won't go wrong either way. I've been very happy with my program (as have my co-residents it seems).
