See the problem with saying that LSE Econ students are Oxbridge rejects is that one is assuming that they are of a lower calibre than Cambridge students. I don't believe this to be the case; Cambridge don't really care about grades - they base everything on the interview; and rightly so, as most of the learning will be in a similar environment to interviews. However, LSE select on grades, so the two unis are looking for slightly different people. One wants academic excellence; people who will excel in a self-taught environment, the other wants pupils who interview very well, who can discuss ideas and learn from the discussion.
A debate of whether LSE Econ are smarter than Cambs Econ is a debate between the learning style of interactive, tutorial learning over self-taught, learning from books.