Hey Amitanshu, welcome to the forum
I'm in the exact same situation as you (confused about whether I want to do consulting or finance, and have an offer for an Msc finance progam in addition to the LBS MiM).
I can't offer you much advice except that when it comes down to it, LBS's name will likely carry you further in Europe and Asia (from what I've gathered, not so much in North America where I'm from as US has its own share of top business schools
). I recently read in an article that although LBS does not really rank #1 in the world (as claimed by Financial times) in terms of prestige in the minds of employers, it does come in at 10th, which is neverthless quite amazing.
Regardless, LBS is still a very prestigious business school with a great reputation! I spoke to an ex executive of a major ibank and according to him, it would be hard and unlikely for HR to ding a resume with the LBS name stamped on it. Right now I'm about 70% leaning towards LBS for these reasons.
In terms of job placements, I'm planning on calling the admissions office next week to ask. I will let you know! You should do the same for SSE, since the program itself should be the most reliable source.
Good luck with your decision making! I've been confused and restless for the past week! ahaha