It seems that most people favour LSE over Cambridge- but that's to be expected on an LSE thread- I'm sure the same question under the Cambridge University thread would produce a different result.
The LSE degree is more mathematical than the Cambridge one. I'm not entirely sure about the comment of LSE's course being more "relevant".
In terms of one course being "better" than the other, however, well...... that really depends on what you want to do and specifically which company you want to work in- different firms have their own preferences as do the individuals who recruit you (and you can't control some of these factors).
In truth, employers will be looking at other things on your CV; different skills and experiences are what's going to stand out as well as the classification of your degree.
One shouldn't worry too much about how prospective employers perceive the image of you chosen University (not when it gets to this high level anyway).... go where you think you will feel comfortable.