Got an offer from LSE myself and didn´t apply to Oxford.
If I had and Oxford would´ve let me in, I´d go for Oxford all the way. Not because LSE is bad (we both know very well it is not- in fact everyone knows), but because it is Oxford (1st in the world).
Finances of course are a thing, but then you have Oxford employability after you graduate (then again LSE employability is not really that inferior, I suspect...)
As you might have noticed my argumentation is not rational at all, but if I were you there would be a very loud voice in my head screaming "It´s OXFORD, you retard! Take it."
But, if you can lead a happy life knowing you got into Oxford and didn´t go, then I guess it´s LSE.