1. Brand (specially in India in the longer run) - I think MIT pips Kellogg here. The alumni base for Sloan and Kellogg might be very similar, but the broader MIT university carries a LOT of weight. Having said that, I've interacted with quite a few consultants from Kellogg who have successfully transitioned back to India. In fact, a couple had very successful exits from MBBs after coming to India. To me, there isn't a huge gap between the two. It's just that the word 'MIT' carries the wow feeling within non-business/layman circles.
2. Placement opportunities (specially in strategy consulting) - Both will get you there. Kellogg is a consulting powerhouse (might be self selection).
3. Friendly culture (during the two years at school) - Kellogg's student body is very friendly and 'collaborative'. Also, I can't say this with certainty, but MIT's is less so.
4. Option to pursue dual degree in policy with HKS - As KF mentioned, I'd give a point to MIT here.
So, you probably knew this, but it's more or less a choice between MIT's slight prestige advantage and Kellogg's culture/student body. If I were you, I'd make sure that I'm happy for two years and therefore, my vote goes to Kellogg.
P.S - I haven't factored HKS here. Are you still exploring the option or pretty set on doing the dual degree?