I am also considering these two schools. Hard choice.
Here is my brief analysis that I did recently based on LBS and CBS employment reports (based on the list of top employers and bolded/not bolded employers in the overall list of employers):
I took ten global banks (BAML, Barclays, Citi, Credit Suisse, Deutsche Bank, HSBC, Goldman Sachs, JPMorgan, Morgan Stanley, UBS) and McKinsey, BCG, Bain.
LBS (% of class): banks - 8,1%, MBB - 16,2%
CBS (% of class): banks - 11,1%, MBB - 14,8%;
CBS has the highest percent (for aforementioned 10 banks) among all top business schools (excluding H/S/W - no such statistics in their employment reports).
I am not interested in PE and VC, so, you have to do your own research

I think their percent is too small to make a meaningful conclusion.
BTW, percent of class that goes to finance: CBS - 35%, LBS - 28%.
So, CBS is more about finance than LBS.
If you are indifferent between US and UK, then, obviously, US is a bigger market, which with aforementioned information tilts you towards CBS.
P. S. I think you should also include Wharton on your list