MBA8717
I would then take into consideration several aspects to make the decision:
1) How big the network and reputation of both schools is in both regions (London and your country). Just considering landing your first job in London, I am not pretty sure you will find it easier at LBS (just considering geography, on campus recruiting possibilities and network). However, I don't think it won't be possible to land a good one from CBS (unless you manage to get an exchange at LBS, it will require plenty of off-campus recruiting from a different continent).
2) How long will you like to stay in London before moving to your home country (As if it is a long time the university where you went will not be as important as your experience)
3) Lifestyle: NYC and London are very different cities with very different lifestyles: which want do you prefer? Also, you mention that your partner will find easier to get a visa to work in the UK (that is another very important factor to consider)
4) Fit: with what students/alumni/culture do you feel a higher fit?
5) Possibility of exchange to LBS from CBS. I know that LBS gives you alumnus status if you do an exchange there during your MBA. It would be interesting to consider how likely is that you get an exchange to LBS from CBS during few months. (However, I will not count on it to make the decision as I assume that exchange will be extremely competitive).
Hope it helps