You're really overthinking it. Think about the following:
- Both places will land you interviews assuming your profile (CV, cover letter, networking) are reasonably robust
- If you're into living in a big city or you think London is for you, go to LSE
- If you want cheaper (and better accommodation) go to Cambridge
- If you want to be in a collegiate environment go to Cambridge
- If you want to be in a smaller city (much smaller) and are up for going to May Balls, gowned formals and being in a much more traditional university then go to Cambridge
- If you really like the mechanics and mathematical aspects of Economics then decide on LSE
- If you like looking at some mechanics and a little bit of the mathematical aspects of Economics and are up for looking at new subjects like Law (Constitutional, Contract, Property) and the way in which economics plays a part in development, real estate, inequality then choose Land Economy
- If you want better teaching, go to Cambridge
- If you want to go into consulting, I think Cambridge would be marginally better
- Satisfaction also seems to be much better at Cambridge
- There are about a 1000 more things to consider but those are the main ones.
Finally, also think about where you achieve the better grades/what will be easier - you want to make sure you're getting solid 2.1's or firsts to be competitive.