I am an international student at both places and will be paying international tuition at both. I have been accepted for BSc Finance at LSE and Business Economics at UCLA.
What, in your opinion, would be a better choice?
Broad question that needs more detail about you to answer,
It partly depends where you come from and presumably plan to return to. A lot of countries (especially in the former British empire) will have higher regard for an LSE than a UCLA degree. (I would also rank finance over business economics, but that depends what you want to do at the end of it.)
For the college experience, life in LA will be very different to that in
London. Have you visited both cities before?
For US vs UK degrees in general, you have the 4-year more broad degree vs the 3-year more focused one. Do you have a preference between those?