FORE and KJ Somaiya are both excellent. The curriculum is designed in consultation with industry leaders and the growing demands of the industry as an ongoing process at FORE, making it relevant to the workplace. FORE has a strong connection with the corporate world and is a preferred destination for recruiters because it provides value to the recruiter as well. The average CTC offered by both institutes is nearly identical - FORE: INR 14.04 LPA & KJS: INR 12.28 LPA.
If you are not from Mumbai, you must also consider the cost of living. Delhi/NCR is always less expensive than Mumbai.
To begin with, there is no such thing as a "flagship" in college, so you may not have heard anything about going to KJ Somaiya for marketing or that it is best for HR or Finance. All programs, specialized or super-specialized, are treated equally, and top-tier faculty are available for all courses.
There is almost nothing significant on which any of the programs can be graded. It all comes down to personal preference. If you want to work in International Business (finance or marketing), go for it; if you want to learn everything there is to know about finance, financial services are the way to go. In any case, you won't be short on opportunities.