I would pick Kellogg in your case. If the money was comparable at Stern, it could be up for discussion, but it isn't easy to rationalize given your specific situation.
IMO, I would only pick the following programs over a non-HS M7 for specific reasons (barring relocation constraints, personality preferences, case method format etc):
Haas: General tech goals, preferably on the west coast.
SOM: Non-profit goals, or international goals vs M7 programs with weaker int'l reputations (Booth, Kellogg)
Stern: NYC IB goals, preferably for EBs.
Fuqua: Healthcare goals.
Now, finance is a rather broad career goal. If you're looking at IB or IM, there might not be a tangible difference in recruiting outcomes, or even a slight advantage to Stern for the earlier category, if candidate profiles are normalized. However, Kellogg has a stronger rep for PE. This is something to think about if PE is a tangential career goal for you as well.
There should be no difference for BB recruiting between the two programs, aside from the lower time commitment at Kellogg. At Stern, you will have to be ready to skip class for a coffee chat on short notice. Being in the city has considerable drawbacks but can also make your profile stand out if you would have otherwise not been as competitive for IB recruiting. There is more nuance with group-specific recruiting (for example, going outside Goldman Nat Res from Stern due to alumni presence) and EBs (Elite Boutiques). I won't expound on it further as I am uncertain about your career goals.
Then again, you have a full scholarship at Kellogg; I highly suspect that your resume will be at the top of every pile and that you can receive the same offer with much less work. If you can spare the time, send an app in for HSW.
Edit: Noticed the follow-up post with career goals. All the more reason to pick Kellogg. If you are looking into HF recruiting for FO roles, I would strongly consider applying to HSW. I personally went through the process with a few firms and did not get past first round interviews; how much of that was due to my own background, performance, or school is difficult to ascertain, but when the chances are already miniscule you should try to improve the odds as much as possible.